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				<div lang="en" dir="ltr" class="mw-content-ltr"><div class="dablink">"Stock option" redirects here. For the employee incentive, see <a href="http://pandapedia.com/wiki/Employee_stock_option" title="Employee stock option">Employee stock option</a>.</div>
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<p>In <a href="http://pandapedia.com/wiki/Finance" title="Finance">finance</a>, an <b>option</b> is a <a href="http://pandapedia.com/wiki/Derivative_(finance)" title="Derivative (finance)">derivative</a> <a href="http://pandapedia.com/wiki/Financial_instrument" title="Financial instrument">financial instrument</a> that specifies a contract between two parties for a future transaction on an asset at a reference price (the strike).<sup id="cite_ref-Pascucci_0-0" class="reference"><a href="#cite_note-Pascucci-0"><span>[</span>1<span>]</span></a></sup> The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the corresponding obligation to fulfil the transaction. The price of an option derives from the difference between the reference price and the value of the <i><a href="http://pandapedia.com/wiki/Underlying" title="Underlying">underlying</a></i> asset (commonly a <a href="http://pandapedia.com/wiki/Stock" title="Stock">stock</a>, a <a href="http://pandapedia.com/wiki/Bond_(finance)" title="Bond (finance)">bond</a>, a <a href="http://pandapedia.com/wiki/Currency" title="Currency">currency</a> or a <a href="http://pandapedia.com/wiki/Futures_contract" title="Futures contract">futures contract</a>) plus a premium based on the time remaining until the expiration of the option. Other types of options exist, and options can in principle be created for any type of valuable asset.</p>
<p>An option which conveys the right to buy something at a specific price is called a <b><a href="http://pandapedia.com/wiki/Call_option" title="Call option">call</a></b>; an option which conveys the right to sell something at a specific price is called a <b><a href="http://pandapedia.com/wiki/Put_option" title="Put option">put</a></b>. The reference price at which the underlying asset may be traded is called the <a href="http://pandapedia.com/wiki/Strike_price" title="Strike price">strike price</a> or exercise price. The process of activating an option and thereby trading the underlying at the agreed-upon price is referred to as <i><a href="http://pandapedia.com/wiki/Exercise_(options)" title="Exercise (options)">exercising</a></i> it. Most options have an <a href="http://pandapedia.com/wiki/Expiration_(options)" title="Expiration (options)">expiration date</a>. If the option is not exercised by the expiration date, it becomes void and worthless.<sup id="cite_ref-Pascucci_0-1" class="reference"><a href="#cite_note-Pascucci-0"><span>[</span>1<span>]</span></a></sup></p>
<p>In return for assuming the obligation, called <i>writing</i> the option, the originator of the option collects a payment, the <i>premium</i>, from the buyer. The writer of an option must make good on delivering (or receiving) the underlying asset or its cash equivalent, if the option is exercised.</p>
<p>An option can usually be sold by its original buyer to another party. Many options are created in standardized form and traded on an anonymous <a href="http://pandapedia.com/wiki/Exchange_(organized_market)" title="Exchange (organized market)">options exchange</a> among the general public, while other <a href="http://pandapedia.com/wiki/Over-the-counter_(finance)" title="Over-the-counter (finance)">over-the-counter</a> options are customized ad hoc to the desires of the buyer, usually by an <a href="http://pandapedia.com/wiki/Investment_bank" title="Investment bank" class="mw-redirect">investment bank</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span>[</span>2<span>]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span>[</span>3<span>]</span></a></sup></p>
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<h2>Contents</h2>
</div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="#Contract_specifications"><span class="tocnumber">1</span> <span class="toctext">Contract specifications</span></a></li>
<li class="toclevel-1 tocsection-2"><a href="#Types"><span class="tocnumber">2</span> <span class="toctext">Types</span></a>
<ul>
<li class="toclevel-2 tocsection-3"><a href="#Exchange-traded_options"><span class="tocnumber">2.1</span> <span class="toctext">Exchange-traded options</span></a></li>
<li class="toclevel-2 tocsection-4"><a href="#Over-the-counter"><span class="tocnumber">2.2</span> <span class="toctext">Over-the-counter</span></a></li>
<li class="toclevel-2 tocsection-5"><a href="#Other_option_types"><span class="tocnumber">2.3</span> <span class="toctext">Other option types</span></a></li>
<li class="toclevel-2 tocsection-6"><a href="#Option_styles"><span class="tocnumber">2.4</span> <span class="toctext">Option styles</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-7"><a href="#Valuation_models"><span class="tocnumber">3</span> <span class="toctext">Valuation models</span></a>
<ul>
<li class="toclevel-2 tocsection-8"><a href="#Black.E2.80.93Scholes"><span class="tocnumber">3.1</span> <span class="toctext">Black–Scholes</span></a></li>
<li class="toclevel-2 tocsection-9"><a href="#Stochastic_volatility_models"><span class="tocnumber">3.2</span> <span class="toctext">Stochastic volatility models</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-10"><a href="#Model_implementation"><span class="tocnumber">4</span> <span class="toctext">Model implementation</span></a>
<ul>
<li class="toclevel-2 tocsection-11"><a href="#Analytic_techniques"><span class="tocnumber">4.1</span> <span class="toctext">Analytic techniques</span></a></li>
<li class="toclevel-2 tocsection-12"><a href="#Binomial_tree_pricing_model"><span class="tocnumber">4.2</span> <span class="toctext">Binomial tree pricing model</span></a></li>
<li class="toclevel-2 tocsection-13"><a href="#Monte_Carlo_models"><span class="tocnumber">4.3</span> <span class="toctext">Monte Carlo models</span></a></li>
<li class="toclevel-2 tocsection-14"><a href="#Finite_difference_models"><span class="tocnumber">4.4</span> <span class="toctext">Finite difference models</span></a></li>
<li class="toclevel-2 tocsection-15"><a href="#Other_models"><span class="tocnumber">4.5</span> <span class="toctext">Other models</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-16"><a href="#Risks"><span class="tocnumber">5</span> <span class="toctext">Risks</span></a>
<ul>
<li class="toclevel-2 tocsection-17"><a href="#Example"><span class="tocnumber">5.1</span> <span class="toctext">Example</span></a></li>
<li class="toclevel-2 tocsection-18"><a href="#Pin_risk"><span class="tocnumber">5.2</span> <span class="toctext">Pin risk</span></a></li>
<li class="toclevel-2 tocsection-19"><a href="#Counterparty_risk"><span class="tocnumber">5.3</span> <span class="toctext">Counterparty risk</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-20"><a href="#Trading"><span class="tocnumber">6</span> <span class="toctext">Trading</span></a></li>
<li class="toclevel-1 tocsection-21"><a href="#The_basic_trades_of_traded_stock_options_.28American_style.29"><span class="tocnumber">7</span> <span class="toctext">The basic trades of traded stock options (American style)</span></a>
<ul>
<li class="toclevel-2 tocsection-22"><a href="#Long_call"><span class="tocnumber">7.1</span> <span class="toctext">Long call</span></a></li>
<li class="toclevel-2 tocsection-23"><a href="#Long_put"><span class="tocnumber">7.2</span> <span class="toctext">Long put</span></a></li>
<li class="toclevel-2 tocsection-24"><a href="#Short_call"><span class="tocnumber">7.3</span> <span class="toctext">Short call</span></a></li>
<li class="toclevel-2 tocsection-25"><a href="#Short_put"><span class="tocnumber">7.4</span> <span class="toctext">Short put</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-26"><a href="#Option_strategies"><span class="tocnumber">8</span> <span class="toctext">Option strategies</span></a></li>
<li class="toclevel-1 tocsection-27"><a href="#Historical_uses_of_options"><span class="tocnumber">9</span> <span class="toctext">Historical uses of options</span></a></li>
<li class="toclevel-1 tocsection-28"><a href="#See_also"><span class="tocnumber">10</span> <span class="toctext">See also</span></a></li>
<li class="toclevel-1 tocsection-29"><a href="#References"><span class="tocnumber">11</span> <span class="toctext">References</span></a></li>
<li class="toclevel-1 tocsection-30"><a href="#Further_reading"><span class="tocnumber">12</span> <span class="toctext">Further reading</span></a></li>
<li class="toclevel-1 tocsection-31"><a href="#External_links"><span class="tocnumber">13</span> <span class="toctext">External links</span></a></li>
</ul>
</td>
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</table>
<h2> <span class="mw-headline" id="Contract_specifications">Contract specifications</span></h2>
<p>Every financial option is a contract between the two counterparties with the terms of the option specified in a <a href="http://pandapedia.com/wiki/Term_sheet" title="Term sheet">term sheet</a>. Option contracts may be quite complicated; however, at minimum, they usually contain the following specifications:<sup id="cite_ref-occ_3-0" class="reference"><a href="#cite_note-occ-3"><span>[</span>4<span>]</span></a></sup></p>
<ul>
<li>whether the option holder has the right to buy (a <a href="http://pandapedia.com/wiki/Call_option" title="Call option">call option</a>) or the right to sell (a <a href="http://pandapedia.com/wiki/Put_option" title="Put option">put option</a>)</li>
<li>the quantity and class of the <a href="http://pandapedia.com/wiki/Underlying" title="Underlying">underlying</a> asset(s) (e.g., 100 shares of XYZ Co. B stock)</li>
<li>the <a href="http://pandapedia.com/wiki/Strike_price" title="Strike price">strike price</a>, also known as the exercise price, which is the price at which the underlying transaction will occur upon <a href="http://pandapedia.com/wiki/Exercise_(options)" title="Exercise (options)">exercise</a></li>
<li>the <a href="http://pandapedia.com/wiki/Expiration_(options)" title="Expiration (options)">expiration</a> date, or expiry, which is the last date the option can be exercised</li>
<li>the <a href="http://pandapedia.com/wiki/Settlement_(finance)" title="Settlement (finance)">settlement terms</a>, for instance whether the writer must deliver the actual asset on exercise, or may simply tender the equivalent cash amount</li>
<li>the terms by which the option is quoted in the market to convert the quoted price into the actual premium&#160;– the total amount paid by the holder to the writer</li>
</ul>
<h2> <span class="mw-headline" id="Types">Types</span></h2>
<p>The Options can be classified into following types:</p>
<h3> <span class="mw-headline" id="Exchange-traded_options">Exchange-traded options</span></h3>
<ul>
<li><b>Exchange-traded options</b> (also called "listed options") are a class of <a href="http://pandapedia.com/wiki/Derivative_(finance)#OTC_and_exchange-traded" title="Derivative (finance)">exchange-traded derivatives</a>. Exchange traded options have standardized contracts, and are settled through a <a href="http://pandapedia.com/wiki/Clearing_house_(finance)" title="Clearing house (finance)">clearing house</a> with fulfillment guaranteed by the credit of the exchange. Since the contracts are standardized, accurate pricing models are often available. Exchange-traded options include:<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span>[</span>5<span>]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span>[</span>6<span>]</span></a></sup>
<ul>
<li><a href="http://pandapedia.com/wiki/Stock_options" title="Stock options" class="mw-redirect">stock options</a>,</li>
<li><a href="http://pandapedia.com/wiki/Bond_option" title="Bond option">bond options</a> and other <a href="http://pandapedia.com/wiki/Interest_rate_derivative" title="Interest rate derivative">interest rate options</a></li>
<li><a href="http://pandapedia.com/wiki/Stock_market_index_option" title="Stock market index option">stock market index options</a> or, simply, index options and</li>
<li><a href="http://pandapedia.com/wiki/Options_on_futures_contracts" title="Options on futures contracts" class="mw-redirect">options on futures contracts</a></li>
<li><a href="http://pandapedia.com/wiki/Callable_bull/bear_contract" title="Callable bull/bear contract">callable bull/bear contract</a></li>
</ul>
</li>
</ul>
<h3> <span class="mw-headline" id="Over-the-counter">Over-the-counter</span></h3>
<ul>
<li><b><a href="http://pandapedia.com/wiki/Over-the-counter_(finance)" title="Over-the-counter (finance)">Over-the-counter</a> options</b> (OTC options, also called "dealer options") are traded between two private parties, and are not listed on an exchange. The terms of an OTC option are unrestricted and may be individually tailored to meet any business need. In general, at least one of the counterparties to an OTC option is a well-capitalized institution. Option types commonly traded over the counter include:</li>
</ul>
<ol>
<li>interest rate options</li>
<li>currency cross rate options, and</li>
<li>options on <a href="http://pandapedia.com/wiki/Swap_(finance)" title="Swap (finance)">swaps</a> or <a href="http://pandapedia.com/wiki/Swaption" title="Swaption">swaptions</a>.</li>
</ol>
<h3> <span class="mw-headline" id="Other_option_types">Other option types</span></h3>
<p>Another important class of options, particularly in the U.S., are <a href="http://pandapedia.com/wiki/Employee_stock_option" title="Employee stock option">employee stock options</a>, which are awarded by a company to their employees as a form of incentive compensation. Other types of options exist in many financial contracts, for example <a href="http://pandapedia.com/wiki/Option_(law)" title="Option (law)">real estate options</a> are often used to assemble large parcels of land, and <a href="http://pandapedia.com/wiki/Prepayment_of_loan" title="Prepayment of loan">prepayment</a> options are usually included in <a href="http://pandapedia.com/wiki/Mortgage_loan" title="Mortgage loan">mortgage loans</a>. However, many of the valuation and risk management principles apply across all financial options.</p>
<h3> <span class="mw-headline" id="Option_styles">Option styles</span></h3>
<div class="rellink relarticle mainarticle">Main article: <a href="http://pandapedia.com/wiki/Option_style" title="Option style">Option style</a></div>
<p>Naming conventions are used to help identify properties common to many different types of options. These include:</p>
<ul>
<li><b>European</b> option&#160;– an option that may only be <a href="http://pandapedia.com/wiki/Exercise_(options)" title="Exercise (options)">exercised</a> on <a href="http://pandapedia.com/wiki/Expiration_(options)" title="Expiration (options)">expiration</a>.</li>
<li><b>American</b> option&#160;– an option that may be exercised on any trading day on or before expiry.</li>
<li><b>Bermudan</b> option&#160;– an option that may be exercised only on specified dates on or before expiration.</li>
<li><b>Barrier</b> option&#160;– any option with the general characteristic that the underlying security's price must pass a certain level or "barrier" before it can be exercised.</li>
<li><b>Exotic</b> option&#160;– any of a broad category of options that may include complex financial structures.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span>[</span>7<span>]</span></a></sup></li>
<li><b>Vanilla</b> option&#160;– any option that is not exotic.</li>
</ul>
<h2> <span class="mw-headline" id="Valuation_models">Valuation models</span></h2>
<div class="rellink relarticle mainarticle">Main article: <a href="http://pandapedia.com/wiki/Valuation_of_options" title="Valuation of options">Valuation of options</a></div>
<p>The value of an option can be estimated using a variety of quantitative techniques based on the concept of <a href="http://pandapedia.com/wiki/Risk_neutral" title="Risk neutral">risk neutral</a> pricing and using <a href="http://pandapedia.com/wiki/Stochastic_calculus" title="Stochastic calculus">stochastic calculus</a>. The most basic model is the <a href="http://pandapedia.com/wiki/Black%E2%80%93Scholes" title="Black–Scholes">Black–Scholes</a> model. More sophisticated models are used to model the <a href="http://pandapedia.com/wiki/Volatility_smile" title="Volatility smile">volatility smile</a>. These models are implemented using a variety of numerical techniques.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span>[</span>8<span>]</span></a></sup> In general, standard option valuation models depend on the following factors:</p>
<ul>
<li>The current market price of the underlying security,</li>
<li>the <a href="http://pandapedia.com/wiki/Strike_price" title="Strike price">strike price</a> of the option, particularly in relation to the current market price of the underlying (in the money vs. out of the money),</li>
<li>the cost of holding a position in the underlying security, including interest and dividends,</li>
<li>the time to <a href="http://pandapedia.com/wiki/Expiration_(options)" title="Expiration (options)">expiration</a> together with any restrictions on when exercise may occur, and</li>
<li>an estimate of the future <a href="http://pandapedia.com/wiki/Volatility_(finance)" title="Volatility (finance)">volatility</a> of the underlying security's price over the life of the option.</li>
</ul>
<p>More advanced models can require additional factors, such as an estimate of how volatility changes over time and for various underlying price levels, or the dynamics of stochastic interest rates.</p>
<p>The following are some of the principal valuation techniques used in practice to evaluate option contracts.</p>
<h3> <span class="mw-headline" id="Black.E2.80.93Scholes">Black–Scholes</span></h3>
<div class="rellink relarticle mainarticle">Main article: <a href="http://pandapedia.com/wiki/Black%E2%80%93Scholes" title="Black–Scholes">Black–Scholes</a></div>
<p>Following early work by <a href="http://pandapedia.com/wiki/Louis_Bachelier" title="Louis Bachelier">Louis Bachelier</a> and later work by <a href="http://pandapedia.com/wiki/Edward_O._Thorp" title="Edward O. Thorp">Edward O. Thorp</a>, <a href="http://pandapedia.com/wiki/Fischer_Black" title="Fischer Black">Fischer Black</a> and <a href="http://pandapedia.com/wiki/Myron_Scholes" title="Myron Scholes">Myron Scholes</a> made a major breakthrough by deriving a differential equation that must be satisfied by the price of any derivative dependent on a non-dividend-paying stock. By employing the technique of constructing a risk neutral portfolio that replicates the returns of holding an option, Black and Scholes produced a closed-form solution for a European option's theoretical price.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span>[</span>9<span>]</span></a></sup> At the same time, the model generates <a href="http://pandapedia.com/wiki/Greeks_(finance)" title="Greeks (finance)">hedge parameters</a> necessary for effective risk management of option holdings. While the ideas behind the Black–Scholes model were ground-breaking and eventually led to <a href="http://pandapedia.com/wiki/Myron_Scholes" title="Myron Scholes">Scholes</a> and <a href="http://pandapedia.com/wiki/Robert_C._Merton" title="Robert C. Merton">Merton</a> receiving the <a href="http://pandapedia.com/wiki/Swedish_Central_Bank" title="Swedish Central Bank" class="mw-redirect">Swedish Central Bank</a>'s associated <a href="http://pandapedia.com/wiki/The_Sveriges_Riksbank_Prize_in_Economic_Sciences_in_Memory_of_Alfred_Nobel" title="The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel" class="mw-redirect">Prize for Achievement in Economics</a> (a.k.a., the <a href="http://pandapedia.com/wiki/Nobel_Prize" title="Nobel Prize">Nobel Prize</a> in Economics),<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span>[</span>10<span>]</span></a></sup> the application of the model in actual options trading is clumsy because of the assumptions of continuous (or no) dividend payment, constant volatility, and a constant interest rate. Nevertheless, the Black–Scholes model is still one of the most important methods and foundations for the existing financial market in which the result is within the reasonable range.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span>[</span>11<span>]</span></a></sup></p>
<h3> <span class="mw-headline" id="Stochastic_volatility_models">Stochastic volatility models</span></h3>
<div class="rellink relarticle mainarticle">Main article: <a href="http://pandapedia.com/wiki/Heston_model" title="Heston model">Heston model</a></div>
<p>Since the market crash of 1987, it has been observed that market <a href="http://pandapedia.com/wiki/Implied_volatility" title="Implied volatility">implied volatility</a> for options of lower strike prices are typically higher than for higher strike prices, suggesting that volatility is stochastic, varying both for time and for the price level of the underlying security. <a href="http://pandapedia.com/wiki/Stochastic_volatility" title="Stochastic volatility">Stochastic volatility</a> models have been developed including one developed by <a href="http://pandapedia.com/wiki/Heston_model" title="Heston model">S.L. Heston</a>.<sup id="cite_ref-gatheral_11-0" class="reference"><a href="#cite_note-gatheral-11"><span>[</span>12<span>]</span></a></sup> One principal advantage of the Heston model is that it can be solved in closed-form, while other stochastic volatility models require complex numerical methods.<sup id="cite_ref-gatheral_11-1" class="reference"><a href="#cite_note-gatheral-11"><span>[</span>12<span>]</span></a></sup></p>
<div class="rellink boilerplate seealso">See also: <a href="http://pandapedia.com/wiki/SABR_Volatility_Model" title="SABR Volatility Model" class="mw-redirect">SABR Volatility Model</a></div>
<h2> <span class="mw-headline" id="Model_implementation">Model implementation</span></h2>
<div class="rellink">Further information: <a href="http://pandapedia.com/wiki/Valuation_of_options" title="Valuation of options">Valuation of options</a></div>
<p>Once a valuation model has been chosen, there are a number of different techniques used to take the mathematical models to implement the models.</p>
<h3> <span class="mw-headline" id="Analytic_techniques">Analytic techniques</span></h3>
<p>In some cases, one can take the <a href="http://pandapedia.com/wiki/Mathematical_model" title="Mathematical model">mathematical model</a> and using analytical methods develop <a href="http://pandapedia.com/wiki/Closed-form_expression" title="Closed-form expression">closed form solutions</a> such as <a href="http://pandapedia.com/wiki/Black%E2%80%93Scholes" title="Black–Scholes">Black–Scholes</a> and the <a href="http://pandapedia.com/wiki/Black_model" title="Black model">Black model</a>. The resulting solutions are readily computable, as are their <a href="http://pandapedia.com/wiki/Greeks_(finance)" title="Greeks (finance)">"Greeks"</a>.</p>
<h3> <span class="mw-headline" id="Binomial_tree_pricing_model">Binomial tree pricing model</span></h3>
<div class="rellink relarticle mainarticle">Main article: <a href="http://pandapedia.com/wiki/Binomial_options_pricing_model" title="Binomial options pricing model">Binomial options pricing model</a></div>
<p>Closely following the derivation of Black and Scholes, <a href="http://pandapedia.com/wiki/John_C._Cox" title="John C. Cox" class="mw-redirect">John Cox</a>, <a href="http://pandapedia.com/wiki/Stephen_Ross_(economist)" title="Stephen Ross (economist)">Stephen Ross</a> and <a href="http://pandapedia.com/wiki/Mark_Rubinstein" title="Mark Rubinstein">Mark Rubinstein</a> developed the original version of the <a href="http://pandapedia.com/wiki/Binomial_options_pricing_model" title="Binomial options pricing model">binomial options pricing model</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span>[</span>13<span>]</span></a></sup> <sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span>[</span>14<span>]</span></a></sup> It models the dynamics of the option's theoretical value for <a href="http://pandapedia.com/wiki/Discrete" title="Discrete">discrete</a> time intervals over the option's life. The model starts with a binomial tree of discrete future possible underlying stock prices. By constructing a riskless portfolio of an option and stock (as in the Black–Scholes model) a simple formula can be used to find the option price at each node in the tree. This value can approximate the theoretical value produced by Black Scholes, to the desired degree of precision. However, the binomial model is considered more accurate than Black–Scholes because it is more flexible; e.g., discrete future dividend payments can be modeled correctly at the proper forward time steps, and <a href="http://pandapedia.com/wiki/American_option" title="American option" class="mw-redirect">American options</a> can be modeled as well as European ones. Binomial models are widely used by professional option traders. The <a href="http://pandapedia.com/wiki/Trinomial_tree" title="Trinomial tree">Trinomial tree</a> is a similar model, allowing for an up, down or stable path; although considered more accurate, particularly when fewer time-steps are modelled, it is less commonly used as its implementation is more complex.</p>
<h3> <span class="mw-headline" id="Monte_Carlo_models">Monte Carlo models</span></h3>
<div class="rellink relarticle mainarticle">Main article: <a href="http://pandapedia.com/wiki/Monte_Carlo_methods_for_option_pricing" title="Monte Carlo methods for option pricing">Monte Carlo methods for option pricing</a></div>
<p>For many classes of options, traditional valuation techniques are <a href="http://pandapedia.com/wiki/Tractability" title="Tractability" class="mw-redirect">intractable</a> because of the complexity of the instrument. In these cases, a Monte Carlo approach may often be useful. Rather than attempt to solve the differential equations of motion that describe the option's value in relation to the underlying security's price, a Monte Carlo model uses <a href="http://pandapedia.com/wiki/Monte_Carlo_simulation" title="Monte Carlo simulation" class="mw-redirect">simulation</a> to generate random price paths of the underlying asset, each of which results in a payoff for the option. The average of these payoffs can be discounted to yield an <a href="http://pandapedia.com/wiki/Expectation_value" title="Expectation value" class="mw-redirect">expectation value</a> for the option.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span>[</span>15<span>]</span></a></sup> Note though, that despite its flexibility, using simulation for <a href="http://pandapedia.com/wiki/American_option" title="American option" class="mw-redirect">American styled options</a> is somewhat more complex than for lattice based models.</p>
<h3> <span class="mw-headline" id="Finite_difference_models">Finite difference models</span></h3>
<div class="rellink relarticle mainarticle">Main article: <a href="http://pandapedia.com/wiki/Finite_difference_methods_for_option_pricing" title="Finite difference methods for option pricing">Finite difference methods for option pricing</a></div>
<p>The equations used to model the option are often expressed as <a href="http://pandapedia.com/wiki/Partial_differential_equation" title="Partial differential equation">partial differential equations</a> (see for example <a href="http://pandapedia.com/wiki/Black%E2%80%93Scholes_formula#Black.E2.80.93Scholes_PDE" title="Black–Scholes formula" class="mw-redirect">Black–Scholes PDE</a>). Once expressed in this form, a <a href="http://pandapedia.com/wiki/Finite_difference_method" title="Finite difference method">finite difference model</a> can be derived, and the valuation obtained. A number of implementations of finite difference methods exist for option valuation, including: <a href="http://pandapedia.com/wiki/Explicit_method" title="Explicit method" class="mw-redirect">explicit finite difference</a>, <a href="http://pandapedia.com/wiki/Implicit_method" title="Implicit method" class="mw-redirect">implicit finite difference</a> and the <a href="http://pandapedia.com/wiki/Crank-Nicholson_method" title="Crank-Nicholson method" class="mw-redirect">Crank-Nicholson method</a>. A trinomial tree option pricing model can be shown to be a simplified application of the explicit finite difference method. Although the finite difference approach is mathematically sophisticated, it is particularly useful where changes are assumed over time in model inputs&#160;– for example dividend yield, risk free rate, or volatility, or some combination of these&#160;– that are not <a href="http://pandapedia.com/wiki/Tractable" title="Tractable">tractable</a> in closed form.</p>
<h3> <span class="mw-headline" id="Other_models">Other models</span></h3>
<p>Other numerical implementations which have been used to value options include <a href="http://pandapedia.com/wiki/Finite_element_method" title="Finite element method">finite element methods</a>. Additionally, various <a href="http://pandapedia.com/wiki/Short_rate_model" title="Short rate model" class="mw-redirect">short rate models</a> have been developed for the valuation of <a href="http://pandapedia.com/wiki/Interest_rate_derivatives" title="Interest rate derivatives" class="mw-redirect">interest rate derivatives</a>, <a href="http://pandapedia.com/wiki/Bond_option" title="Bond option">bond options</a> and <a href="http://pandapedia.com/wiki/Swaption" title="Swaption">swaptions</a>. These, similarly, allow for closed-form, lattice-based, and simulation-based modelling, with corresponding advantages and considerations.</p>
<h2> <span class="mw-headline" id="Risks">Risks</span></h2>
<p>As with all securities, trading options entails the risk of the option's value changing over time. However, unlike traditional securities, the <a href="http://pandapedia.com/wiki/Stock_option_return" title="Stock option return">return</a> from holding an option varies non-linearly with the value of the underlying and other factors. Therefore, the risks associated with holding options are more complicated to understand and predict.</p>
<p>In general, the change in the value of an option can be derived from <a href="http://pandapedia.com/wiki/Ito%27s_lemma" title="Ito's lemma" class="mw-redirect">Ito's lemma</a> as:</p>
<dl>
<dd>
<dl>
<dd><img class="tex" alt="dC=\Delta dS + \Gamma \frac{dS^2}{2} + \kappa d\sigma + \theta dt \," src="//upload.wikimedia.org/wikipedia/en/math/b/3/4/b34b23687787d995ba945c67cfebfded.png" /></dd>
</dl>
</dd>
</dl>
<p>where the <a href="http://pandapedia.com/wiki/Greeks_(finance)" title="Greeks (finance)">Greeks</a> <span class="texhtml" dir="ltr">Δ</span>, <span class="texhtml" dir="ltr">Γ</span>, <span class="texhtml" dir="ltr">κ</span> and <span class="texhtml" dir="ltr">θ</span> are the standard hedge parameters calculated from an option valuation model, such as <a href="http://pandapedia.com/wiki/Black%E2%80%93Scholes" title="Black–Scholes">Black–Scholes</a>, and <span class="texhtml" dir="ltr"><i>d</i><i>S</i></span>, <span class="texhtml" dir="ltr"><i>d</i>σ</span> and <span class="texhtml" dir="ltr"><i>d</i><i>t</i></span> are unit changes in the underlying's price, the underlying's volatility and time, respectively.</p>
<p>Thus, at any point in time, one can estimate the risk inherent in holding an option by calculating its hedge parameters and then estimating the expected change in the model inputs, <span class="texhtml" dir="ltr"><i>d</i><i>S</i></span>, <span class="texhtml" dir="ltr"><i>d</i>σ</span> and <span class="texhtml" dir="ltr"><i>d</i><i>t</i></span>, provided the changes in these values are small. This technique can be used effectively to understand and manage the risks associated with standard options. For instance, by offsetting a holding in an option with the quantity <span class="texhtml" dir="ltr">− Δ</span> of shares in the underlying, a trader can form a <a href="http://pandapedia.com/wiki/Delta_neutral" title="Delta neutral">delta neutral</a> portfolio that is hedged from loss for small changes in the underlying's price. The corresponding price sensitivity formula for this portfolio <span class="texhtml" dir="ltr">Π</span> is:</p>
<dl>
<dd>
<dl>
<dd><img class="tex" alt="d\Pi=\Delta dS  + \Gamma \frac{dS^2}{2} + \kappa d\sigma + \theta dt = \Gamma \frac{dS^2}{2} + \kappa d\sigma + \theta dt\," src="//upload.wikimedia.org/wikipedia/en/math/2/1/9/2197ad8d301eeb757886dfd1ecbb2339.png" /></dd>
</dl>
</dd>
</dl>
<h3> <span class="mw-headline" id="Example">Example</span></h3>
<p>A call option expiring in 99 days on 100 shares of XYZ stock is struck at $50, with XYZ currently trading at $48. With future realized volatility over the life of the option estimated at 25%, the theoretical value of the option is $1.89. The hedge parameters <span class="texhtml" dir="ltr">Δ</span>, <span class="texhtml" dir="ltr">Γ</span>, <span class="texhtml" dir="ltr">κ</span>, <span class="texhtml" dir="ltr">θ</span> are (0.439, 0.0631, 9.6, and −0.022), respectively. Assume that on the following day, XYZ stock rises to $48.5 and volatility falls to 23.5%. We can calculate the estimated value of the call option by applying the hedge parameters to the new model inputs as:</p>
<dl>
<dd>
<dl>
<dd><img class="tex" alt="dC = (0.439 \cdot 0.5) + \left(0.0631 \cdot \frac{0.5^2}{2} \right) + (9.6 \cdot -0.015) + (-0.022 \cdot 1) = 0.0614" src="//upload.wikimedia.org/wikipedia/en/math/4/4/6/4461f6ee1174b57d5cd6e9d35b807f5b.png" /></dd>
</dl>
</dd>
</dl>
<p>Under this scenario, the value of the option increases by $0.0614 to $1.9514, realizing a profit of $6.14. Note that for a delta neutral portfolio, whereby the trader had also sold 44 shares of XYZ stock as a hedge, the net loss under the same scenario would be ($15.86).</p>
<h3> <span class="mw-headline" id="Pin_risk">Pin risk</span></h3>
<div class="rellink relarticle mainarticle">Main article: <a href="http://pandapedia.com/wiki/Pin_risk" title="Pin risk" class="mw-redirect">Pin risk</a></div>
<p>A special situation called <a href="http://pandapedia.com/wiki/Pin_risk_(option)" title="Pin risk (option)" class="mw-redirect">pin risk</a> can arise when the underlying closes at or very close to the option's strike value on the last day the option is traded prior to expiration. The option writer (seller) may not know with certainty whether or not the option will actually be exercised or be allowed to expire worthless. Therefore, the option writer may end up with a large, unwanted residual position in the underlying when the markets open on the next trading day after expiration, regardless of their best efforts to avoid such a residual.</p>
<h3> <span class="mw-headline" id="Counterparty_risk">Counterparty risk</span></h3>
<p>A further, often ignored, risk in derivatives such as options is counterparty risk. In an option contract this risk is that the seller won't sell or buy the underlying asset as agreed. The risk can be minimized by using a financially strong intermediary able to make good on the trade, but in a major panic or crash the number of defaults can overwhelm even the strongest intermediaries.</p>
<h2> <span class="mw-headline" id="Trading">Trading</span></h2>
<p>The most common way to trade options is via standardized options contracts that are listed by various <a href="http://pandapedia.com/wiki/Futures_exchange" title="Futures exchange">futures and options exchanges</a>. <sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span>[</span>16<span>]</span></a></sup> Listings and prices are tracked and can be looked up by <a href="http://pandapedia.com/wiki/Option_symbol" title="Option symbol">ticker symbol</a>. By publishing continuous, live markets for option prices, an exchange enables independent parties to engage in <a href="http://pandapedia.com/wiki/Price_discovery" title="Price discovery">price discovery</a> and execute transactions. As an intermediary to both sides of the transaction, the benefits the exchange provides to the transaction include:</p>
<ul>
<li>fulfillment of the contract is backed by the credit of the exchange, which typically has the highest <a href="http://pandapedia.com/wiki/Bond_rating" title="Bond rating" class="mw-redirect">rating</a> (AAA),</li>
<li>counterparties remain anonymous,</li>
<li>enforcement of market regulation to ensure fairness and transparency, and</li>
<li>maintenance of orderly markets, especially during fast trading conditions.</li>
</ul>
<p><a href="http://pandapedia.com/wiki/Over-the-counter_(finance)" title="Over-the-counter (finance)">Over-the-counter</a> options contracts are not traded on exchanges, but instead between two independent parties. Ordinarily, at least one of the counterparties is a well-capitalized institution. By avoiding an exchange, users of OTC options can narrowly tailor the terms of the option contract to suit individual business requirements. In addition, OTC option transactions generally do not need to be advertised to the market and face little or no regulatory requirements. However, OTC counterparties must establish credit lines with each other, and conform to each others clearing and settlement procedures.</p>
<p>With few exceptions,<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span>[</span>17<span>]</span></a></sup> there are no <a href="http://pandapedia.com/wiki/Secondary_markets" title="Secondary markets" class="mw-redirect">secondary markets</a> for <a href="http://pandapedia.com/wiki/Employee_stock_options" title="Employee stock options" class="mw-redirect">employee stock options</a>. These must either be exercised by the original grantee or allowed to expire worthless.</p>
<h2> <span class="mw-headline" id="The_basic_trades_of_traded_stock_options_.28American_style.29">The basic trades of traded stock options (American style)</span></h2>
<p>These trades are described from the point of view of a speculator. If they are combined with other positions, they can also be used in hedging. An option contract in US markets usually represents 100 shares of the underlying security.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span>[</span>18<span>]</span></a></sup></p>
<h3> <span class="mw-headline" id="Long_call">Long call</span></h3>
<div class="thumb tright">
<div class="thumbinner" style="width:202px;"><a href="http://pandapedia.com/wiki/File:Long_call_option.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Long_call_option.svg/200px-Long_call_option.svg.png" width="200" height="131" class="thumbimage" /></a>
<div class="thumbcaption">
<div class="magnify"><a href="http://pandapedia.com/wiki/File:Long_call_option.svg" class="internal" title="Enlarge"><img src="//bits.wikimedia.org/skins-1.18/common/images/magnify-clip.png" width="15" height="11" alt="" /></a></div>
Payoff from buying a call.</div>
</div>
</div>
<p>A trader who believes that a stock's price will <b>increase</b> might buy the right to purchase the stock (a <a href="http://pandapedia.com/wiki/Call_option" title="Call option">call option</a>) rather than just purchase the stock itself. He would have no obligation to buy the stock, only the right to do so until the expiration date. If the stock price at expiration is above the exercise price by more than the premium (price) paid, he will profit. If the stock price at expiration is lower than the exercise price, he will let the call contract expire worthless, and only lose the amount of the premium. A trader might buy the option instead of shares, because for the same amount of money, he can control (<a href="http://pandapedia.com/wiki/Leverage_(finance)" title="Leverage (finance)">leverage</a>) a much larger number of shares.</p>
<div style="clear:both;"></div>
<h3> <span class="mw-headline" id="Long_put">Long put</span></h3>
<div class="thumb tright">
<div class="thumbinner" style="width:202px;"><a href="http://pandapedia.com/wiki/File:Long_put_option.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Long_put_option.svg/200px-Long_put_option.svg.png" width="200" height="131" class="thumbimage" /></a>
<div class="thumbcaption">
<div class="magnify"><a href="http://pandapedia.com/wiki/File:Long_put_option.svg" class="internal" title="Enlarge"><img src="//bits.wikimedia.org/skins-1.18/common/images/magnify-clip.png" width="15" height="11" alt="" /></a></div>
Payoff from buying a put.</div>
</div>
</div>
<p>A trader who believes that a stock's price will <b>decrease</b> can buy the right to sell the stock at a fixed price (a <a href="http://pandapedia.com/wiki/Put_option" title="Put option">put option</a>). He will be under no obligation to sell the stock, but has the right to do so until the expiration date. If the stock price at expiration is below the exercise price by more than the premium paid, he will profit. If the stock price at expiration is above the exercise price, he will let the put contract expire worthless and only lose the premium paid.</p>
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<h3> <span class="mw-headline" id="Short_call">Short call</span></h3>
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Payoff from writing a call.</div>
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<p>A trader who believes that a stock price will <b>decrease</b> can sell the stock short or instead sell, or "write," a call. The trader selling a call has an obligation to sell the stock to the call buyer at the buyer's option. If the stock price decreases, the short call position will make a profit in the amount of the premium. If the stock price increases over the exercise price by more than the amount of the premium, the short will lose money, with the potential loss unlimited.</p>
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<h3> <span class="mw-headline" id="Short_put">Short put</span></h3>
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Payoff from writing a put.</div>
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<p>A trader who believes that a stock price will <b>increase</b> can buy the stock or instead sell, or "write", a put. The trader selling a put has an obligation to buy the stock from the put buyer at the put buyer's option. If the stock price at expiration is above the exercise price, the short put position will make a profit in the amount of the premium. If the stock price at expiration is below the exercise price by more than the amount of the premium, the trader will lose money, with the potential loss being up to the full value of the stock. A benchmark index for the performance of a cash-secured short put option position is the <a href="http://pandapedia.com/wiki/CBOE_S%26P_500_PutWrite_Index" title="CBOE S&amp;P 500 PutWrite Index">CBOE S&amp;P 500 PutWrite Index</a> (ticker PUT).</p>
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<h2> <span class="mw-headline" id="Option_strategies">Option strategies</span></h2>
<div class="rellink relarticle mainarticle">Main article: <a href="http://pandapedia.com/wiki/Option_strategies" title="Option strategies" class="mw-redirect">Option strategies</a></div>
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<div class="thumbinner" style="width:202px;"><a href="http://pandapedia.com/wiki/File:Long_butterfly_option.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Long_butterfly_option.svg/200px-Long_butterfly_option.svg.png" width="200" height="131" class="thumbimage" /></a>
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Payoffs from buying a butterfly spread.</div>
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Payoffs from selling a straddle.</div>
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<div class="thumbinner" style="width:202px;"><a href="http://pandapedia.com/wiki/File:Covered_Call.jpg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/6/67/Covered_Call.jpg/200px-Covered_Call.jpg" width="200" height="137" class="thumbimage" /></a>
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Payoffs from a covered call.</div>
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<p>Combining any of the four basic kinds of option trades (possibly with different exercise prices and maturities) and the two basic kinds of stock trades (long and short) allows a variety of <a href="http://pandapedia.com/wiki/Options_strategies" title="Options strategies">options strategies</a>. Simple strategies usually combine only a few trades, while more complicated strategies can combine several.</p>
<p>Strategies are often used to engineer a particular risk profile to movements in the underlying security. For example, buying a <a href="http://pandapedia.com/wiki/Butterfly_(options)" title="Butterfly (options)">butterfly</a> spread (long one X1 call, short two X2 calls, and long one X3 call) allows a trader to profit if the stock price on the expiration date is near the middle exercise price, X2, and does not expose the trader to a large loss.</p>
<p>An <a href="http://pandapedia.com/wiki/Iron_condor" title="Iron condor">Iron condor</a> is a strategy that is similar to a butterfly spread, but with different strikes for the short options&#160;– offering a larger likelihood of profit but with a lower net credit compared to the butterfly spread.</p>
<p>Selling a <a href="http://pandapedia.com/wiki/Straddle" title="Straddle">straddle</a> (selling both a put and a call at the same exercise price) would give a trader a greater profit than a butterfly if the final stock price is near the exercise price, but might result in a large loss.</p>
<p>Similar to the straddle is the <a href="http://pandapedia.com/wiki/Strangle_(options)" title="Strangle (options)">strangle</a> which is also constructed by a call and a put, but whose strikes are different, reducing the net debit of the trade, but also reducing the risk of loss in the trade.</p>
<p>One well-known strategy is the <a href="http://pandapedia.com/wiki/Covered_call" title="Covered call">covered call</a>, in which a trader buys a stock (or holds a previously-purchased long stock position), and sells a call. If the stock price rises above the exercise price, the call will be exercised and the trader will get a fixed profit. If the stock price falls, the call will not be exercised, and any loss incurred to the trader will be partially offset by the premium received from selling the call. Overall, the payoffs match the payoffs from selling a put. This relationship is known as <a href="http://pandapedia.com/wiki/Put-call_parity" title="Put-call parity" class="mw-redirect">put-call parity</a> and offers insights for financial theory. A benchmark index for the performance of a <a href="http://pandapedia.com/wiki/Buy-write" title="Buy-write">buy-write</a> strategy is the <a href="http://pandapedia.com/wiki/CBOE_S%26P_500_BuyWrite_Index" title="CBOE S&amp;P 500 BuyWrite Index">CBOE S&amp;P 500 BuyWrite Index</a> (ticker symbol BXM).</p>
<h2> <span class="mw-headline" id="Historical_uses_of_options">Historical uses of options</span></h2>
<p>Contracts similar to options are believed to have been used since ancient times. In the <a href="http://pandapedia.com/wiki/Real_estate" title="Real estate">real estate</a> market, call options have long been used to assemble large parcels of land from separate owners; e.g., a developer pays for the right to buy several adjacent plots, but is not obligated to buy these plots and might not unless he can buy all the plots in the entire parcel. Film or theatrical producers often buy the right&#160;— but not the obligation&#160;— to dramatize a specific book or script. <a href="http://pandapedia.com/wiki/Line_of_credit" title="Line of credit">Lines of credit</a> give the potential borrower the right&#160;— but not the obligation&#160;— to borrow within a specified time period.</p>
<p>Many choices, or embedded options, have traditionally been included in <a href="http://pandapedia.com/wiki/Bond_(finance)" title="Bond (finance)">bond</a> contracts. For example many bonds are <a href="http://pandapedia.com/wiki/Convertible_bond" title="Convertible bond">convertible</a> into common stock at the buyer's option, or may be called (bought back) at specified prices at the issuer's option. <a href="http://pandapedia.com/wiki/Mortgage_loan" title="Mortgage loan">Mortgage</a> borrowers have long had the option to repay the loan early, which corresponds to a callable bond option.</p>
<p>In London, puts and "refusals" (calls) first became well-known trading instruments in the 1690s during the reign of <a href="http://pandapedia.com/wiki/William_and_Mary" title="William and Mary">William and Mary</a>.<sup id="cite_ref-Global_18-0" class="reference"><a href="#cite_note-Global-18"><span>[</span>19<span>]</span></a></sup></p>
<p><i>Privileges</i> were options sold over the counter in nineteenth century America, with both puts and calls on shares offered by specialized dealers. Their exercise price was fixed at a rounded-off market price on the day or week that the option was bought, and the expiry date was generally three months after purchase. They were not traded in secondary markets.</p>
<p>Supposedly the first option buyer in the world was the <a href="http://pandapedia.com/wiki/Ancient_Greece" title="Ancient Greece">ancient Greek</a> mathematician and philosopher <a href="http://pandapedia.com/wiki/Thales" title="Thales">Thales</a> of Miletus. On a certain occasion, it was predicted that the season's <a href="http://pandapedia.com/wiki/Olive" title="Olive">olive</a> harvest would be larger than usual, and during the off-season he acquired the right to use a number of olive presses the following spring. When spring came and the olive harvest was larger than expected he exercised his options and then rented the presses out at much higher price than he paid for his 'option'.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span>[</span>20<span>]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span>[</span>21<span>]</span></a></sup></p>
<h2> <span class="mw-headline" id="See_also">See also</span></h2>
<ul>
<li><a href="http://pandapedia.com/wiki/American_Stock_Exchange" title="American Stock Exchange">American Stock Exchange</a></li>
<li><a href="http://pandapedia.com/wiki/Chicago_Board_Options_Exchange" title="Chicago Board Options Exchange">Chicago Board Options Exchange</a></li>
<li><a href="http://pandapedia.com/wiki/Eurex" title="Eurex">Eurex</a></li>
<li><a href="http://pandapedia.com/wiki/Euronext.liffe" title="Euronext.liffe" class="mw-redirect">Euronext.liffe</a></li>
<li><a href="http://pandapedia.com/wiki/International_Securities_Exchange" title="International Securities Exchange">International Securities Exchange</a></li>
<li><a href="http://pandapedia.com/wiki/NYSE_Arca" title="NYSE Arca">NYSE Arca</a></li>
<li><a href="http://pandapedia.com/wiki/Philadelphia_Stock_Exchange" title="Philadelphia Stock Exchange">Philadelphia Stock Exchange</a></li>
<li><a href="http://pandapedia.com/wiki/LEAPS_(finance)" title="LEAPS (finance)">LEAPS (finance)</a></li>
<li><a href="http://pandapedia.com/wiki/Real_options_analysis" title="Real options analysis" class="mw-redirect">Real options analysis</a></li>
<li><a href="http://pandapedia.com/wiki/PnL_Explained" title="PnL Explained">PnL Explained</a></li>
</ul>
<h2> <span class="mw-headline" id="References">References</span></h2>
<div class="reflist references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;">
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<li id="cite_note-2"><b><a href="#cite_ref-2">^</a></b> <span class="citation" id="CITEREFHull2005">Hull, John C. (2005), <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL2Zhbi56aGFuZy5nbC9lY3JlZi9vcHRpb25z"><i>Options, Futures and Other Derivatives (excerpt by Fan Zhang)</i></a> (6th ed.), Pg 6: Prentice-Hall, <a href="http://pandapedia.com/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a>&#160;<a href="http://pandapedia.com/wiki/Special:BookSources/0131499084" title="Special:BookSources/0131499084">0131499084</a><span class="printonly">, <a rel="nofollow" class="external free" href="/redirect?url=aHR0cDovL2Zhbi56aGFuZy5nbC9lY3JlZi9vcHRpb25z">http://fan.zhang.gl/ecref/options</a></span></span><span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Options%2C+Futures+and+Other+Derivatives+%28excerpt+by+Fan+Zhang%29&amp;rft.aulast=Hull&amp;rft.aufirst=John+C.&amp;rft.au=Hull%2C%26%2332%3BJohn+C.&amp;rft.date=2005&amp;rft.edition=6th&amp;rft.place=Pg+6&amp;rft.pub=Prentice-Hall&amp;rft.isbn=0131499084&amp;rft_id=http%3A%2F%2Ffan.zhang.gl%2Fecref%2Foptions&amp;rfr_id=info:sid/en.wikipedia.org:Option_(finance)"><span style="display: none;">&#160;</span></span></li>
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<li id="cite_note-8"><b><a href="#cite_ref-8">^</a></b> Black, Fischer and Myron S. Scholes. "The Pricing of Options and Corporate Liabilities," <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5qb3VybmFscy51Y2hpY2Fnby5lZHUvSlBFLw%3D%3D">Journal of Political Economy</a>, 81 (3), 637–654 (1973).</li>
<li id="cite_note-9"><b><a href="#cite_ref-9">^</a></b> <span class="citation" id="CITEREFDas2006">Das, Satyajit (2006), <i>Traders, Guns &amp; Money: Knowns and unknowns in the dazzling world of derivatives</i> (6th ed.), Prentice-Hall, Chapter 1 'Financial WMDs – derivatives demagoguery,' p.22, <a href="http://pandapedia.com/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a>&#160;<a href="http://pandapedia.com/wiki/Special:BookSources/978-0-273-70474-4" title="Special:BookSources/978-0-273-70474-4">978-0-273-70474-4</a></span><span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Traders%2C+Guns+%26+Money%3A+Knowns+and+unknowns+in+the+dazzling+world+of+derivatives&amp;rft.aulast=Das&amp;rft.aufirst=Satyajit&amp;rft.au=Das%2C%26%2332%3BSatyajit&amp;rft.date=2006&amp;rft.edition=6th&amp;rft.pub=Prentice-Hall%2C+Chapter+1+%27Financial+WMDs+%E2%80%93+derivatives+demagoguery%2C%27+p.22&amp;rft.isbn=978-0-273-70474-4&amp;rfr_id=info:sid/en.wikipedia.org:Option_(finance)"><span style="display: none;">&#160;</span></span></li>
<li id="cite_note-10"><b><a href="#cite_ref-10">^</a></b> <span class="citation" id="CITEREFHull2005">Hull, John C. (2005), <i>Options, Futures and Other Derivatives</i> (6th ed.), Prentice-Hall, <a href="http://pandapedia.com/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a>&#160;<a href="http://pandapedia.com/wiki/Special:BookSources/0131499084" title="Special:BookSources/0131499084">0131499084</a></span><span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Options%2C+Futures+and+Other+Derivatives&amp;rft.aulast=Hull&amp;rft.aufirst=John+C.&amp;rft.au=Hull%2C%26%2332%3BJohn+C.&amp;rft.date=2005&amp;rft.edition=6th&amp;rft.pub=Prentice-Hall&amp;rft.isbn=0131499084&amp;rfr_id=info:sid/en.wikipedia.org:Option_(finance)"><span style="display: none;">&#160;</span></span></li>
<li id="cite_note-gatheral-11">^ <a href="#cite_ref-gatheral_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-gatheral_11-1"><sup><i><b>b</b></i></sup></a> <span class="citation" id="CITEREFJim_Gatheral2006">Jim Gatheral (2006), <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5hbWF6b24uY29tL1ZvbGF0aWxpdHktU3VyZmFjZS1QcmFjdGl0aW9uZXJzLUd1aWRlLUZpbmFuY2UvZHAvMDQ3MTc5MjUxOQ%3D%3D"><i>The Volatility Surface, A Practitioner's Guide</i></a>, Wiley Finance, <a href="http://pandapedia.com/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a>&#160;<a href="http://pandapedia.com/wiki/Special:BookSources/978-0471792512" title="Special:BookSources/978-0471792512">978-0471792512</a><span class="printonly">, <a rel="nofollow" class="external free" href="/redirect?url=aHR0cDovL3d3dy5hbWF6b24uY29tL1ZvbGF0aWxpdHktU3VyZmFjZS1QcmFjdGl0aW9uZXJzLUd1aWRlLUZpbmFuY2UvZHAvMDQ3MTc5MjUxOQ%3D%3D">http://www.amazon.com/Volatility-Surface-Practitioners-Guide-Finance/dp/0471792519</a></span></span><span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=The+Volatility+Surface%2C+A+Practitioner%27s+Guide&amp;rft.aulast=Jim+Gatheral&amp;rft.au=Jim+Gatheral&amp;rft.date=2006&amp;rft.pub=Wiley+Finance&amp;rft.isbn=978-0471792512&amp;rft_id=http%3A%2F%2Fwww.amazon.com%2FVolatility-Surface-Practitioners-Guide-Finance%2Fdp%2F0471792519&amp;rfr_id=info:sid/en.wikipedia.org:Option_(finance)"><span style="display: none;">&#160;</span></span></li>
<li id="cite_note-12"><b><a href="#cite_ref-12">^</a></b> <a href="http://pandapedia.com/wiki/John_C._Cox" title="John C. Cox" class="mw-redirect">Cox JC</a>, <a href="http://pandapedia.com/wiki/Stephen_Ross_(economist)" title="Stephen Ross (economist)">Ross SA</a> and <a href="http://pandapedia.com/wiki/Mark_Rubinstein" title="Mark Rubinstein">Rubinstein M</a>. 1979. Options pricing: a simplified approach, <a href="http://pandapedia.com/wiki/Journal_of_Financial_Economics" title="Journal of Financial Economics">Journal of Financial Economics</a>, 7:229–263.<a rel="nofollow" class="external autonumber" href="/redirect?url=aHR0cDovL3d3dy5pbi10aGUtbW9uZXkuY29tL2FydGFuZHBhcC9PcHRpb24lMjBQcmljaW5nJTIwLSUyMEElMjBTaW1wbGlmaWVkJTIwQXBwcm9hY2guZG9j">[1]</a></li>
<li id="cite_note-13"><b><a href="#cite_ref-13">^</a></b> <span class="citation" id="CITEREFCoxRubinstein1985"><a href="http://pandapedia.com/wiki/John_C._Cox" title="John C. Cox" class="mw-redirect">Cox, John C.</a>; <a href="http://pandapedia.com/wiki/Mark_Rubinstein" title="Mark Rubinstein">Rubinstein, Mark</a> (1985), <i>Options Markets</i>, Prentice-Hall, Chapter 5</span><span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Options+Markets&amp;rft.aulast=Cox&amp;rft.aufirst=John+C.&amp;rft.au=Cox%2C%26%2332%3BJohn+C.&amp;rft.au=Rubinstein%2C%26%2332%3BMark&amp;rft.date=1985&amp;rft.pub=Prentice-Hall&amp;rfr_id=info:sid/en.wikipedia.org:Option_(finance)"><span style="display: none;">&#160;</span></span></li>
<li id="cite_note-14"><b><a href="#cite_ref-14">^</a></b> <span class="citation" id="CITEREFCrack2004">Crack, Timothy Falcon (2004), <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5CYXNpY0JsYWNrU2Nob2xlcy5jb20v"><i>Basic Black–Scholes: Option Pricing and Trading</i></a> (1st ed.), pp. 91–102, <a href="http://pandapedia.com/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a>&#160;<a href="http://pandapedia.com/wiki/Special:BookSources/0-9700552-2-6" title="Special:BookSources/0-9700552-2-6">0-9700552-2-6</a><span class="printonly">, <a rel="nofollow" class="external free" href="/redirect?url=aHR0cDovL3d3dy5CYXNpY0JsYWNrU2Nob2xlcy5jb20v">http://www.BasicBlackScholes.com/</a></span></span><span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Basic+Black%E2%80%93Scholes%3A+Option+Pricing+and+Trading&amp;rft.aulast=Crack&amp;rft.aufirst=Timothy+Falcon&amp;rft.au=Crack%2C%26%2332%3BTimothy+Falcon&amp;rft.date=2004&amp;rft.edition=1st&amp;rft.place=pp.+91%E2%80%93102&amp;rft.isbn=0-9700552-2-6&amp;rft_id=http%3A%2F%2Fwww.BasicBlackScholes.com%2F&amp;rfr_id=info:sid/en.wikipedia.org:Option_(finance)"><span style="display: none;">&#160;</span></span></li>
<li id="cite_note-15"><b><a href="#cite_ref-15">^</a></b> <span class="citation" id="CITEREFHarris2003">Harris, Larry (2003), <i>Trading and Exchanges</i>, Oxford University Press, pp.26–27</span><span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Trading+and+Exchanges&amp;rft.aulast=Harris&amp;rft.aufirst=Larry&amp;rft.au=Harris%2C%26%2332%3BLarry&amp;rft.date=2003&amp;rft.pub=Oxford+University+Press&amp;rfr_id=info:sid/en.wikipedia.org:Option_(finance)"><span style="display: none;">&#160;</span></span></li>
<li id="cite_note-16"><b><a href="#cite_ref-16">^</a></b> <span class="citation" id="CITEREFElinor_Mills2006">Elinor Mills (2006-12-12), <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL25ld3MuY29tLmNvbS9Hb29nbGUrdW52ZWlscyt1bm9ydGhvZG94K3N0b2NrK29wdGlvbithdWN0aW9uLzIxMDAtMTAzMF8zLTYxNDMyMjcuaHRtbA%3D%3D"><i>Google unveils unorthodox stock option auction</i></a>, CNet<span class="printonly">, <a rel="nofollow" class="external free" href="/redirect?url=aHR0cDovL25ld3MuY29tLmNvbS9Hb29nbGUrdW52ZWlscyt1bm9ydGhvZG94K3N0b2NrK29wdGlvbithdWN0aW9uLzIxMDAtMTAzMF8zLTYxNDMyMjcuaHRtbA%3D%3D">http://news.com.com/Google+unveils+unorthodox+stock+option+auction/2100-1030_3-6143227.html</a></span><span class="reference-accessdate">, retrieved 2007-06-19</span></span><span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Google+unveils+unorthodox+stock+option+auction&amp;rft.aulast=Elinor+Mills&amp;rft.au=Elinor+Mills&amp;rft.date=2006-12-12&amp;rft.pub=CNet&amp;rft_id=http%3A%2F%2Fnews.com.com%2FGoogle%2Bunveils%2Bunorthodox%2Bstock%2Boption%2Bauction%2F2100-1030_3-6143227.html&amp;rfr_id=info:sid/en.wikipedia.org:Option_(finance)"><span style="display: none;">&#160;</span></span></li>
<li id="cite_note-17"><b><a href="#cite_ref-17">^</a></b> <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL2ludmVzdC1mYXEuY29tL2NiYy9kZXJpdi1vcHRpb24tYmFzaWNzLmh0bWw%3D">invest-faq</a> or <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy53ZnUuZWR1L35wYWxtaXRhci9MYXcmYW1wO1ZhbHVhdGlvbi9jaGFwdGVyJTIwNC80LTQtMS5odG0%3D">Law &amp; Valuation</a> for typical size of option contract</li>
<li id="cite_note-Global-18"><b><a href="#cite_ref-Global_18-0">^</a></b> <span class="citation" id="CITEREFSmith2003">Smith, B. Mark (2003), <i>History of the Global Stock Market from Ancient Rome to Silicon Valley</i>, University of Chicago Press, pp.&#160;20, <a href="http://pandapedia.com/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a>&#160;<a href="http://pandapedia.com/wiki/Special:BookSources/0-226-76404-4" title="Special:BookSources/0-226-76404-4">0-226-76404-4</a></span><span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=History+of+the+Global+Stock+Market+from+Ancient+Rome+to+Silicon+Valley&amp;rft.aulast=Smith&amp;rft.aufirst=B.+Mark&amp;rft.au=Smith%2C%26%2332%3BB.+Mark&amp;rft.date=2003&amp;rft.pages=pp.%26nbsp%3B20&amp;rft.pub=University+of+Chicago+Press&amp;rft.isbn=0-226-76404-4&amp;rfr_id=info:sid/en.wikipedia.org:Option_(finance)"><span style="display: none;">&#160;</span></span></li>
<li id="cite_note-19"><b><a href="#cite_ref-19">^</a></b> Mattias Sander. Bondesson's Representation of the Variance Gamma Model and Monte Carlo Option Pricing. Lunds Tekniska Högskola 2008</li>
<li id="cite_note-20"><b><a href="#cite_ref-20">^</a></b> Aristotle. Politics.</li>
</ol>
</div>
<h2> <span class="mw-headline" id="Further_reading">Further reading</span></h2>
<ul>
<li>Fischer Black and Myron S. Scholes. "The Pricing of Options and Corporate Liabilities," <i><a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5qb3VybmFscy51Y2hpY2Fnby5lZHUvSlBFLw%3D%3D">Journal of Political Economy</a></i>, 81 (3), 637–654 (1973).</li>
<li>Feldman, Barry and Dhuv Roy. "Passive Options-Based Investment Strategies: The Case of the CBOE S&amp;P 500 BuyWrite Index." <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5paWpvdXJuYWxzLmNvbS9KT0kvZGVmYXVsdC5hc3A%3D"><i>The Journal of Investing</i></a>, (Summer 2005).</li>
<li><a href="http://pandapedia.com/wiki/Hagen_Kleinert" title="Hagen Kleinert">Kleinert, Hagen</a>, <i>Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets</i>, 4th edition, World Scientific (Singapore, 2004); Paperback <a href="http://pandapedia.com/wiki/Special:BookSources/9812381074" class="internal mw-magiclink-isbn">ISBN 981-238-107-4</a> <i>(also available online: <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5waHlzaWsuZnUtYmVybGluLmRlL35rbGVpbmVydC9iNQ%3D%3D">PDF-files</a>)</i></li>
<li>Hill, Joanne, Venkatesh Balasubramanian, Krag (Buzz) Gregory, and Ingrid Tierens. "Finding Alpha via Covered Index Writing." <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5jZmFwdWJzLm9yZy9sb2kvZmFq">Financial Analysts Journal</a>. (Sept.-Oct. 2006). pp.&#160;29–46.</li>
<li>Moran, Matthew. “Risk-adjusted Performance for Derivatives-based Indexes – Tools to Help Stabilize Returns.” <i><a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5pbmRleHVuaXZlcnNlLmNvbS9KT0kv">The Journal of Indexes</a></i>. (Fourth Quarter, 2002) pp.&#160;34 – 40.</li>
<li>Reilly, Frank and Keith C. Brown, Investment Analysis and Portfolio Management, 7th edition, Thompson Southwestern, 2003, pp.&#160;994–5.</li>
<li>Schneeweis, Thomas, and Richard Spurgin. "The Benefits of Index Option-Based Strategies for Institutional Portfolios" <i><a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5paWpvdXJuYWxzLmNvbS9KQUkv">The Journal of Alternative Investments</a></i>, (Spring 2001), pp.&#160;44 – 52.</li>
<li>Whaley, Robert. "Risk and Return of the CBOE BuyWrite Monthly Index" <i><a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5paWpvdXJuYWxzLmNvbS9KT0Qv">The Journal of Derivatives</a></i>, (Winter 2002), pp.&#160;35 – 42.</li>
<li>Bloss, Michael; Ernst, Dietmar; Häcker Joachim (2008): Derivatives&#160;– An authoritative guide to derivatives for financial intermediaries and investors Oldenbourg Verlag München <a href="http://pandapedia.com/wiki/Special:BookSources/9783486586329" class="internal mw-magiclink-isbn">ISBN 978-3-486-58632-9</a></li>
<li>Espen Gaarder Haug &amp; Nassim Nicholas Taleb (2008): <a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3BhcGVycy5zc3JuLmNvbS9zb2wzL3BhcGVycy5jZm0%2FYWJzdHJhY3RfaWQ9MTAxMjA3NSZhbXA7cmVjPTEmYW1wO3NyY2Ficz01Nzcx">"Why We Have Never Used the Black–Scholes–Merton Option Pricing Formula"</a></li>
</ul>
<h2> <span class="mw-headline" id="External_links">External links</span></h2>
<ul>
<li><a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5hY2FkZW1pY2VhcnRoLm9yZy9sZWN0dXJlcy9vcHRpb25zLW1hcmtldHM%3D">Robert Shiller: Video lecture about Option Markets</a></li>
<li><a rel="nofollow" class="external text" href="/redirect?url=aHR0cDovL3d3dy5jYm9lLmNvbS9UcmFkVG9vbC9TeW1ib2xzL1N5bWJvbEVxdWl0eS5hc3B4">List of equities with options</a></li>
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<li><a href="http://pandapedia.com/wiki/Debit_spread" title="Debit spread">Debit spread</a></li>
<li><a href="http://pandapedia.com/wiki/Exercise_(options)" title="Exercise (options)">Exercise</a></li>
<li><a href="http://pandapedia.com/wiki/Expiration_(options)" title="Expiration (options)">Expiration</a></li>
<li><a href="http://pandapedia.com/wiki/Moneyness" title="Moneyness">Moneyness</a></li>
<li><a href="http://pandapedia.com/wiki/Open_interest" title="Open interest">Open interest</a></li>
<li><a href="http://pandapedia.com/wiki/Pin_risk_(option)" title="Pin risk (option)" class="mw-redirect">Pin risk</a></li>
<li><a href="http://pandapedia.com/wiki/Risk-free_rate" title="Risk-free rate" class="mw-redirect">Risk-free rate</a></li>
<li><a href="http://pandapedia.com/wiki/Strike_price" title="Strike price">Strike price</a></li>
<li><a href="http://pandapedia.com/wiki/Greeks_(finance)" title="Greeks (finance)">The Greeks</a></li>
<li><a href="http://pandapedia.com/wiki/Volatility_(finance)" title="Volatility (finance)">Volatility</a></li>
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<li><a href="http://pandapedia.com/wiki/Call_option" title="Call option">Call</a></li>
<li><a href="http://pandapedia.com/wiki/Employee_stock_option" title="Employee stock option">Employee stock option</a></li>
<li><a href="http://pandapedia.com/wiki/Fixed_income" title="Fixed income">Fixed income</a></li>
<li><a href="http://pandapedia.com/wiki/Foreign-exchange_option" title="Foreign-exchange option">FX</a></li>
<li><a href="http://pandapedia.com/wiki/Option_style" title="Option style">Option styles</a></li>
<li><a href="http://pandapedia.com/wiki/Put_option" title="Put option">Put</a></li>
<li><a href="http://pandapedia.com/wiki/Warrant_(finance)" title="Warrant (finance)">Warrants</a></li>
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<li><a href="http://pandapedia.com/wiki/Barrier_option" title="Barrier option">Barrier</a></li>
<li><a href="http://pandapedia.com/wiki/Binary_option" title="Binary option">Binary</a></li>
<li><a href="http://pandapedia.com/wiki/Cliquet" title="Cliquet">Cliquet</a></li>
<li><a href="http://pandapedia.com/wiki/Compound_option" title="Compound option">Compound option</a></li>
<li><a href="http://pandapedia.com/wiki/Forward_start_option" title="Forward start option">Forward start option</a></li>
<li><a href="http://pandapedia.com/wiki/Interest_rate_option" title="Interest rate option">Interest rate option</a></li>
<li><a href="http://pandapedia.com/wiki/Lookback_option" title="Lookback option">Lookback</a></li>
<li><a href="http://pandapedia.com/wiki/Mountain_range_(options)" title="Mountain range (options)">Mountain range</a></li>
<li><a href="http://pandapedia.com/wiki/Rainbow_option" title="Rainbow option">Rainbow option</a></li>
<li><a href="http://pandapedia.com/wiki/Swaption" title="Swaption">Swaption</a></li>
</ul>
</div>
</td>
</tr>
<tr style="height:2px">
<td></td>
</tr>
<tr>
<th scope="row" class="navbox-group" style=";padding-left:0em;padding-right:0em;;">
<div style="padding:0em 0.75em;"><a href="http://pandapedia.com/wiki/Combinations_(finance)" title="Combinations (finance)">Combinations</a></div>
</th>
<td style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;;;" class="navbox-list navbox-even">
<div style="padding:0em 0.25em">
<ul>
<li><a href="http://pandapedia.com/wiki/Collar_(finance)" title="Collar (finance)">Collar</a></li>
<li><a href="http://pandapedia.com/wiki/Fence_(finance)" title="Fence (finance)">Fence</a></li>
<li><a href="http://pandapedia.com/wiki/Iron_butterfly_(options_strategy)" title="Iron butterfly (options strategy)">Iron butterfly</a></li>
<li><a href="http://pandapedia.com/wiki/Iron_condor" title="Iron condor">Iron condor</a></li>
<li><a href="http://pandapedia.com/wiki/Straddle" title="Straddle">Straddle</a></li>
<li><a href="http://pandapedia.com/wiki/Strangle_(options)" title="Strangle (options)">Strangle</a></li>
<li><a href="http://pandapedia.com/wiki/Covered_call" title="Covered call">Covered call</a></li>
<li><a href="http://pandapedia.com/wiki/Protective_put" title="Protective put" class="mw-redirect">Protective put</a></li>
<li><a href="http://pandapedia.com/wiki/Risk_reversal" title="Risk reversal">Risk reversal</a></li>
</ul>
</div>
</td>
</tr>
<tr style="height:2px">
<td></td>
</tr>
<tr>
<th scope="row" class="navbox-group" style=";padding-left:0em;padding-right:0em;;">
<div style="padding:0em 0.75em;"><a href="http://pandapedia.com/wiki/Options_spread" title="Options spread">Options spreads</a></div>
</th>
<td style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;;;" class="navbox-list navbox-odd">
<div style="padding:0em 0.25em">
<ul>
<li><a href="http://pandapedia.com/wiki/Backspread" title="Backspread">Backspread</a></li>
<li><a href="http://pandapedia.com/wiki/Bear_spread" title="Bear spread">Bear spread</a></li>
<li><a href="http://pandapedia.com/wiki/Bull_spread" title="Bull spread">Bull spread</a></li>
<li><a href="http://pandapedia.com/wiki/Box_spread" title="Box spread">Box spread</a></li>
<li><a href="http://pandapedia.com/wiki/Butterfly_(options)" title="Butterfly (options)">Butterfly spread</a></li>
<li><a href="http://pandapedia.com/wiki/Calendar_spread" title="Calendar spread">Calendar spread</a></li>
<li><a href="http://pandapedia.com/wiki/Diagonal_spread" title="Diagonal spread">Diagonal spread</a></li>
<li><a href="http://pandapedia.com/wiki/Ratio_spread" title="Ratio spread">Ratio spread</a></li>
<li><a href="http://pandapedia.com/wiki/Vertical_spread" title="Vertical spread">Vertical spread</a></li>
<li><a href="http://pandapedia.com/wiki/Intermarket_Spread" title="Intermarket Spread">Intermarket Spread</a></li>
</ul>
</div>
</td>
</tr>
<tr style="height:2px">
<td></td>
</tr>
<tr>
<th scope="row" class="navbox-group" style=";padding-left:0em;padding-right:0em;;">
<div style="padding:0em 0.75em;"><a href="http://pandapedia.com/wiki/Valuation_of_options" title="Valuation of options">Valuation of options</a></div>
</th>
<td style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;;;" class="navbox-list navbox-even">
<div style="padding:0em 0.25em">
<ul>
<li><a href="http://pandapedia.com/wiki/Binomial_options_pricing_model" title="Binomial options pricing model">Binomial</a></li>
<li><a href="http://pandapedia.com/wiki/Black_model" title="Black model">Black</a></li>
<li><a href="http://pandapedia.com/wiki/Black%E2%80%93Scholes" title="Black–Scholes">Black–Scholes</a></li>
<li><a href="http://pandapedia.com/wiki/Finite_difference_methods_for_option_pricing" title="Finite difference methods for option pricing">Finite difference</a></li>
<li><a href="http://pandapedia.com/wiki/Foreign-exchange_option#Valuation:_the_Garman.E2.80.93Kohlhagen_model" title="Foreign-exchange option">Garman-Kohlhagen</a></li>
<li><a href="http://pandapedia.com/wiki/Put%E2%80%93call_parity" title="Put–call parity">Put–call parity</a></li>
<li><a href="http://pandapedia.com/wiki/Monte_Carlo_methods_for_option_pricing" title="Monte Carlo methods for option pricing">Simulation</a></li>
<li><a href="http://pandapedia.com/wiki/Trinomial_tree" title="Trinomial tree">Trinomial</a></li>
<li><a href="http://pandapedia.com/wiki/Vanna_Volga" title="Vanna Volga" class="mw-redirect">Vanna Volga method</a></li>
</ul>
</div>
</td>
</tr>
</table>
</td>
</tr>
<tr style="height:2px">
<td></td>
</tr>
<tr>
<th scope="row" class="navbox-group" style=";;"><a href="http://pandapedia.com/wiki/Swap_(finance)" title="Swap (finance)">Swaps</a></th>
<td style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;;;" class="navbox-list navbox-odd hlist">
<div style="padding:0em 0.25em">
<ul>
<li><a href="http://pandapedia.com/wiki/Basis_swap" title="Basis swap">Basis swap</a></li>
<li><a href="http://pandapedia.com/wiki/Conditional_variance_swap" title="Conditional variance swap">Conditional variance swap</a></li>
<li><a href="http://pandapedia.com/wiki/Constant_maturity_swap" title="Constant maturity swap">Constant maturity swap</a></li>
<li><a href="http://pandapedia.com/wiki/Correlation_swap" title="Correlation swap">Correlation swap</a></li>
<li><a href="http://pandapedia.com/wiki/Credit_default_swap" title="Credit default swap">Credit default swap</a></li>
<li><a href="http://pandapedia.com/wiki/Currency_swap" title="Currency swap">Currency swap</a></li>
<li><a href="http://pandapedia.com/wiki/Dividend_swap" title="Dividend swap">Dividend swap</a></li>
<li><a href="http://pandapedia.com/wiki/Equity_swap" title="Equity swap">Equity swap</a></li>
<li><a href="http://pandapedia.com/wiki/Foreign_exchange_swap" title="Foreign exchange swap">Forex swap</a></li>
<li><a href="http://pandapedia.com/wiki/Inflation_swap" title="Inflation swap">Inflation swap</a></li>
<li><a href="http://pandapedia.com/wiki/Interest_rate_swap" title="Interest rate swap">Interest rate swap</a></li>
<li><a href="http://pandapedia.com/wiki/Total_return_swap" title="Total return swap">Total return swap</a></li>
<li><a href="http://pandapedia.com/wiki/Variance_swap" title="Variance swap">Variance swap</a></li>
<li><a href="http://pandapedia.com/wiki/Volatility_swap" title="Volatility swap">Volatility swap</a></li>
</ul>
</div>
</td>
</tr>
<tr style="height:2px">
<td></td>
</tr>
<tr>
<th scope="row" class="navbox-group" style=";;"><a href="http://pandapedia.com/wiki/Forward_contract" title="Forward contract">Forwards</a> and <a href="http://pandapedia.com/wiki/Futures_contract" title="Futures contract">Futures</a></th>
<td style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;;;" class="navbox-list navbox-even hlist">
<div style="padding:0em 0.25em">
<ul>
<li><a href="http://pandapedia.com/wiki/Backwardation" title="Backwardation" class="mw-redirect">Backwardation</a></li>
<li><a href="http://pandapedia.com/wiki/Commodity_futures" title="Commodity futures" class="mw-redirect">Commodity futures</a></li>
<li><a href="http://pandapedia.com/wiki/Contango" title="Contango">Contango</a></li>
<li><a href="http://pandapedia.com/wiki/Currency_future" title="Currency future">Currency future</a></li>
<li><a href="http://pandapedia.com/wiki/Financial_future" title="Financial future">Financial future</a></li>
<li><a href="http://pandapedia.com/wiki/Forward_market" title="Forward market">Forward market</a></li>
<li><a href="http://pandapedia.com/wiki/Forward_price" title="Forward price">Forward price</a></li>
<li><a href="http://pandapedia.com/wiki/Forward_rate" title="Forward rate">Forward rate</a></li>
<li><a href="http://pandapedia.com/wiki/Index_future" title="Index future" class="mw-redirect">Index future</a></li>
<li><a href="http://pandapedia.com/wiki/Interest_rate_future" title="Interest rate future">Interest rate future</a></li>
<li><a href="http://pandapedia.com/wiki/Margin_(finance)" title="Margin (finance)">Margin</a></li>
<li><a href="http://pandapedia.com/wiki/Forward_contract#Spot_-_forward_parity" title="Forward contract">Pricing of Forwards</a></li>
<li><a href="http://pandapedia.com/wiki/Futures_contract#Pricing" title="Futures contract">Pricing of Futures</a></li>
<li><a href="http://pandapedia.com/wiki/Single-stock_futures" title="Single-stock futures">Single-stock futures</a></li>
</ul>
</div>
</td>
</tr>
<tr style="height:2px">
<td></td>
</tr>
<tr>
<th scope="row" class="navbox-group" style=";;">Other derivatives</th>
<td style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;;;" class="navbox-list navbox-odd hlist">
<div style="padding:0em 0.25em">
<ul>
<li><a href="http://pandapedia.com/wiki/Credit_default_option" title="Credit default option">Credit default option</a></li>
<li><a href="http://pandapedia.com/wiki/Credit-linked_note" title="Credit-linked note">CLN</a></li>
<li><a href="http://pandapedia.com/wiki/Contract_for_difference" title="Contract for difference">Contract for difference</a></li>
<li><a href="http://pandapedia.com/wiki/Constant_proportion_portfolio_insurance" title="Constant proportion portfolio insurance">CPPI</a></li>
<li><a href="http://pandapedia.com/wiki/Credit_derivative" title="Credit derivative">Credit derivative</a></li>
<li><a href="http://pandapedia.com/wiki/Equity-Linked_Note" title="Equity-Linked Note">ELN</a></li>
<li><a href="http://pandapedia.com/wiki/Equity_derivative" title="Equity derivative">Equity derivative</a></li>
<li><a href="http://pandapedia.com/wiki/Foreign_exchange_derivative" title="Foreign exchange derivative">Foreign exchange derivative</a></li>
<li><a href="http://pandapedia.com/wiki/Fund_derivative" title="Fund derivative">Fund derivative</a></li>
<li><a href="http://pandapedia.com/wiki/Inflation_derivative" title="Inflation derivative">Inflation derivatives</a></li>
<li><a href="http://pandapedia.com/wiki/Interest_rate_derivative" title="Interest rate derivative">Interest rate derivative</a></li>
<li><a href="http://pandapedia.com/wiki/Power_reverse_dual_currency_note" title="Power reverse dual currency note">PRDC</a></li>
<li><a href="http://pandapedia.com/wiki/Real_estate_derivative" title="Real estate derivative">Real estate derivatives</a></li>
<li><a href="http://pandapedia.com/wiki/Real_options_valuation" title="Real options valuation">Real options</a></li>
</ul>
</div>
</td>
</tr>
<tr style="height:2px">
<td></td>
</tr>
<tr>
<th scope="row" class="navbox-group" style=";;">Market issues</th>
<td style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;;;" class="navbox-list navbox-even hlist">
<div style="padding:0em 0.25em">
<ul>
<li><a href="http://pandapedia.com/wiki/Tax_policy" title="Tax policy">Tax policy</a></li>
<li><a href="http://pandapedia.com/wiki/Consumer_debt" title="Consumer debt">Consumer debt</a></li>
<li><a href="http://pandapedia.com/wiki/Corporate_bond" title="Corporate bond">Corporate debt</a></li>
<li><a href="http://pandapedia.com/wiki/Government_debt" title="Government debt">Government debt</a></li>
<li><a href="http://pandapedia.com/wiki/Late_2000s_recession" title="Late 2000s recession" class="mw-redirect">Late 2000s recession</a></li>
</ul>
</div>
</td>
</tr>
</table>
</td>
</tr>
</table>


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<p><b>Questions for article: </b> an elementary introduction to mathematical finance solution, evaluation de model black and scholes en temps discret (produit derves), text book financial calls puts options, <strong>an elementary introduction to mathematical finance solution</strong></p>

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