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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html">GeneralizedBlackScholesProcess</a></div>
<h1>GeneralizedBlackScholesProcess Class Reference<br>
<small>
[<a class="el" href="group__processes.html">Stochastic processes</a>]</small>
</h1><!-- doxytag: class="QuantLib::GeneralizedBlackScholesProcess" --><!-- doxytag: inherits="QuantLib::StochasticProcess1D" --><code>#include <ql/processes/blackscholesprocess.hpp></code>
<p>
<div class="dynheader">
Inheritance diagram for GeneralizedBlackScholesProcess:</div>
<div class="dynsection">
<p><center><img src="class_quant_lib_1_1_generalized_black_scholes_process__inherit__graph.png" border="0" usemap="#_generalized_black_scholes_process__inherit__map" alt="Inheritance graph"></center>
<map name="_generalized_black_scholes_process__inherit__map">
<area shape="rect" href="class_quant_lib_1_1_black_process.html" title="Black (1976) stochastic process." alt="" coords="5,161,109,188"><area shape="rect" href="class_quant_lib_1_1_black_scholes_merton_process.html" title="Merton (1973) extension to the Black-Scholes stochastic process." alt="" coords="133,161,333,188"><area shape="rect" href="class_quant_lib_1_1_black_scholes_process.html" title="Black-Scholes (1973) stochastic process." alt="" coords="357,161,512,188"><area shape="rect" href="class_quant_lib_1_1_garman_kohlagen_process.html" title="Garman-Kohlhagen (1983) stochastic process." alt="" coords="536,161,720,188"><area shape="rect" href="class_quant_lib_1_1_stochastic_process1_d.html" title="1-dimensional stochastic process" alt="" coords="255,7,412,33"></map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
<p>
<a href="class_quant_lib_1_1_generalized_black_scholes_process-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Generalized Black-Scholes stochastic process.
<p>
This class describes the stochastic process governed by <p class="formulaDsp">
<img class="formulaDsp" alt="\[ dS(t, S) = (r(t) - q(t) - \frac{\sigma(t, S)^2}{2}) dt + \sigma dW_t. \]" src="form_254.png">
<p>
<table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3df0b86a1ef1cf90ccd7403887d2453a"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::GeneralizedBlackScholesProcess" ref="3df0b86a1ef1cf90ccd7403887d2453a" 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))" -->
</td><td class="memItemRight" valign="bottom"><b>GeneralizedBlackScholesProcess</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> > &x0, 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>))</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#f8a1d4ca4369b3009d08291f1c2d7744">time</a> (const <a class="el" href="class_quant_lib_1_1_date.html">Date</a> &) const </td></tr>
<tr><td colspan="2"><div class="groupHeader">StochasticProcess1D interface</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="89d2f497b5fd0d0a0dce2ec82c86e778"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::x0" ref="89d2f497b5fd0d0a0dce2ec82c86e778" args="() const " -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#89d2f497b5fd0d0a0dce2ec82c86e778">x0</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the initial value of the state variable <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#545d33724b1d6d312eb8a17f73571842">drift</a> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#b4d7fe4af7a6dd0ae710c073569821e4">diffusion</a> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ee1aadb67f9085eb8a9fc89604bd8ead">apply</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x0, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> dx) const </td></tr>
<tr><td colspan="2"><div class="groupHeader">Observer interface</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#c5c54df7ed3b930268c8d7752c101725">update</a> ()</td></tr>
<tr><td colspan="2"><div class="groupHeader">Inspectors</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3fdbbd388a2432e1d8d9e94136acfdb8"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::stateVariable" ref="3fdbbd388a2432e1d8d9e94136acfdb8" args="() const " -->
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> > & </td><td class="memItemRight" valign="bottom"><b>stateVariable</b> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d410a408dd37b79578b370b5219dbf80"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::dividendYield" ref="d410a408dd37b79578b370b5219dbf80" args="() const " -->
const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a><br>
< <a class="el" href="class_quant_lib_1_1_yield_term_structure.html">YieldTermStructure</a> > & </td><td class="memItemRight" valign="bottom"><b>dividendYield</b> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="925fdf9de4dd73519b36f975bc7917a8"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::riskFreeRate" ref="925fdf9de4dd73519b36f975bc7917a8" args="() const " -->
const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a><br>
< <a class="el" href="class_quant_lib_1_1_yield_term_structure.html">YieldTermStructure</a> > & </td><td class="memItemRight" valign="bottom"><b>riskFreeRate</b> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="966c6dd76f94ceda5c3a344a8f3e3a8b"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::blackVolatility" ref="966c6dd76f94ceda5c3a344a8f3e3a8b" args="() const " -->
const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a><br>
< <a class="el" href="class_quant_lib_1_1_black_vol_term_structure.html">BlackVolTermStructure</a> > & </td><td class="memItemRight" valign="bottom"><b>blackVolatility</b> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f113ff5ac835cfc641b3ccf701c030b5"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::localVolatility" ref="f113ff5ac835cfc641b3ccf701c030b5" args="() const " -->
const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a><br>
< <a class="el" href="class_quant_lib_1_1_local_vol_term_structure.html">LocalVolTermStructure</a> > & </td><td class="memItemRight" valign="bottom"><b>localVolatility</b> () const </td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="545d33724b1d6d312eb8a17f73571842"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::drift" ref="545d33724b1d6d312eb8a17f73571842" args="(Time t, Real x) const " -->
<div class="memitem">
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> drift </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>x</em></td><td> </td>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
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<p>
<dl compact><dt><b><a class="el" href="todo.html#_todo000045">Possible enhancements:</a></b></dt><dd>revise extrapolation </dd></dl>
<p>Implements <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#6bded8896a46fad4d189950552432cd3">StochasticProcess1D</a>.</p>
</div>
</div><p>
<a class="anchor" name="b4d7fe4af7a6dd0ae710c073569821e4"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::diffusion" ref="b4d7fe4af7a6dd0ae710c073569821e4" 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#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> diffusion </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>x</em></td><td> </td>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
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<div class="memdoc">
<p>
<dl compact><dt><b><a class="el" href="todo.html#_todo000046">Possible enhancements:</a></b></dt><dd>revise extrapolation </dd></dl>
<p>Implements <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#faf479da3baa52185b369071b1689d89">StochasticProcess1D</a>.</p>
</div>
</div><p>
<a class="anchor" name="ee1aadb67f9085eb8a9fc89604bd8ead"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::apply" ref="ee1aadb67f9085eb8a9fc89604bd8ead" args="(Real x0, Real dx) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> apply </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>x0</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>dx</em></td><td> </td>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
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<p>
applies a change to the asset value. By default, it returns <img class="formulaInl" alt="$ x + \Delta x $" src="form_285.png">.
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#905bb2d5a924e5274035b0850c3e04fb">StochasticProcess1D</a>.</p>
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</div><p>
<a class="anchor" name="f8a1d4ca4369b3009d08291f1c2d7744"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::time" ref="f8a1d4ca4369b3009d08291f1c2d7744" args="(const Date &) const " -->
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<td class="memname"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> time </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_date.html">Date</a> & </td>
<td class="paramname"> </td>
<td> ) </td>
<td width="100%"> const<code> [virtual]</code></td>
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<p>
returns the time value corresponding to the given date in the reference system of the stochastic process.<p>
<dl class="note" compact><dt><b>Note:</b></dt><dd>As a number of processes might not need this functionality, a default implementation is given which raises an exception. </dd></dl>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process.html#cb2c915740d2c20c6ee1f5c27b05caef">StochasticProcess</a>.</p>
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<a class="anchor" name="c5c54df7ed3b930268c8d7752c101725"></a><!-- doxytag: member="QuantLib::GeneralizedBlackScholesProcess::update" ref="c5c54df7ed3b930268c8d7752c101725" args="()" -->
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<td class="memname">void update </td>
<td>(</td>
<td class="paramname"> </td>
<td> ) </td>
<td width="100%"><code> [virtual]</code></td>
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<p>
This method must be implemented in derived classes. An instance of Observer does not call this method directly: instead, it will be called by the observables the instance registered with when they need to notify any changes.
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process.html#c5c54df7ed3b930268c8d7752c101725">StochasticProcess</a>.</p>
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