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<a href="#pub-types">Public Types</a> |
<a href="#pub-methods">Public Member Functions</a> </div>
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<div class="title">ExtendedBlackScholesMertonProcess Class Reference<div class="ingroups"><a class="el" href="group__processes.html">Stochastic processes</a></div></div> </div>
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<!-- doxytag: class="QuantLib::ExtendedBlackScholesMertonProcess" --><!-- doxytag: inherits="QuantLib::GeneralizedBlackScholesProcess" -->
<p>experimental Black-Scholes-Merton stochastic process
<a href="class_quant_lib_1_1_extended_black_scholes_merton_process.html#details">More...</a></p>
<p><code>#include <ql/experimental/processes/extendedblackscholesprocess.hpp></code></p>
<div class="dynheader">
Inheritance diagram for ExtendedBlackScholesMertonProcess:</div>
<div class="dyncontent">
<div class="center"><img src="class_quant_lib_1_1_extended_black_scholes_merton_process__inherit__graph.png" border="0" usemap="#_extended_black_scholes_merton_process_inherit__map" alt="Inheritance graph"/></div>
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<p><a href="class_quant_lib_1_1_extended_black_scholes_merton_process-members.html">List of all members.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">enum  </td><td class="memItemRight" valign="bottom"><b>Discretization</b> { <b>Euler</b>,
<b>Milstein</b>,
<b>PredictorCorrector</b>
}</td></tr>
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a945d224778a59f356e087117bd4cb55c"></a><!-- doxytag: member="QuantLib::ExtendedBlackScholesMertonProcess::ExtendedBlackScholesMertonProcess" ref="a945d224778a59f356e087117bd4cb55c" args="(const Handle< Quote > &x0, const Handle< YieldTermStructure > &dividendTS, const Handle< YieldTermStructure > &riskFreeTS, const Handle< BlackVolTermStructure > &blackVolTS, const boost::shared_ptr< discretization > &d=boost::shared_ptr< discretization >(new EulerDiscretization), Discretization evolDisc=Milstein)" -->
 </td><td class="memItemRight" valign="bottom"><b>ExtendedBlackScholesMertonProcess</b> (const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_quote.html">Quote</a> > &<a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#a89d2f497b5fd0d0a0dce2ec82c86e778">x0</a>, const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_yield_term_structure.html">YieldTermStructure</a> > &dividendTS, const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_yield_term_structure.html">YieldTermStructure</a> > &riskFreeTS, const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_black_vol_term_structure.html">BlackVolTermStructure</a> > &blackVolTS, const boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">discretization</a> > &d=boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">discretization</a> >(new <a class="el" href="class_quant_lib_1_1_euler_discretization.html">EulerDiscretization</a>), Discretization evolDisc=Milstein)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extended_black_scholes_merton_process.html#a545d33724b1d6d312eb8a17f73571842">drift</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extended_black_scholes_merton_process.html#ab4d7fe4af7a6dd0ae710c073569821e4">diffusion</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extended_black_scholes_merton_process.html#a28916b3498be74dceb699ad1499a46c0">evolve</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#a89d2f497b5fd0d0a0dce2ec82c86e778">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> dw) const </td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>experimental Black-Scholes-Merton stochastic process </p>
<p>This class allows to choose a built-in discretization scheme </p>
</div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a545d33724b1d6d312eb8a17f73571842"></a><!-- doxytag: member="QuantLib::ExtendedBlackScholesMertonProcess::drift" ref="a545d33724b1d6d312eb8a17f73571842" args="(Time t, Real x) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_extended_black_scholes_merton_process.html#a545d33724b1d6d312eb8a17f73571842">drift</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>t</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>x</em> </td>
</tr>
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<td></td>
<td>)</td>
<td></td><td> const<code> [virtual]</code></td>
</tr>
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<div class="memdoc">
<dl class="todo"><dt><b><a class="el" href="todo.html#_todo000059">Possible enhancements:</a></b></dt><dd>revise extrapolation </dd></dl>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#a545d33724b1d6d312eb8a17f73571842">GeneralizedBlackScholesProcess</a>.</p>
</div>
</div>
<a class="anchor" id="ab4d7fe4af7a6dd0ae710c073569821e4"></a><!-- doxytag: member="QuantLib::ExtendedBlackScholesMertonProcess::diffusion" ref="ab4d7fe4af7a6dd0ae710c073569821e4" args="(Time t, Real x) const " -->
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_extended_black_scholes_merton_process.html#ab4d7fe4af7a6dd0ae710c073569821e4">diffusion</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>t</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>x</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<dl class="todo"><dt><b><a class="el" href="todo.html#_todo000060">Possible enhancements:</a></b></dt><dd>revise extrapolation </dd></dl>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ab4d7fe4af7a6dd0ae710c073569821e4">GeneralizedBlackScholesProcess</a>.</p>
</div>
</div>
<a class="anchor" id="a28916b3498be74dceb699ad1499a46c0"></a><!-- doxytag: member="QuantLib::ExtendedBlackScholesMertonProcess::evolve" ref="a28916b3498be74dceb699ad1499a46c0" args="(Time t0, Real x0, Time dt, Real dw) const " -->
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<tr>
<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_extended_black_scholes_merton_process.html#a28916b3498be74dceb699ad1499a46c0">evolve</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>t0</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>x0</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>dt</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>dw</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [virtual]</code></td>
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<div class="memdoc">
<p>returns the asset value after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_354.png"/> according to the given discretization. By default, it returns </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w \]" src="form_365.png"/>
</p>
<p> where <img class="formulaInl" alt="$ E $" src="form_358.png"/> is the expectation and <img class="formulaInl" alt="$ S $" src="form_212.png"/> the standard deviation. </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#a28916b3498be74dceb699ad1499a46c0">GeneralizedBlackScholesProcess</a>.</p>
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