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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_heston_process.html">HestonProcess</a></div>
<h1>HestonProcess Class Reference<br>
<small>
[<a class="el" href="group__processes.html">Stochastic processes</a>]</small>
</h1><!-- doxytag: class="QuantLib::HestonProcess" --><!-- doxytag: inherits="QuantLib::StochasticProcess" --><code>#include <ql/Processes/hestonprocess.hpp></code>
<p>
Inheritance diagram for HestonProcess:<p><center><img src="class_quant_lib_1_1_heston_process__inherit__graph.png" border="0" usemap="#_heston_process__inherit__map" alt="Inheritance graph"></center>
<map name="_heston_process__inherit__map">
<area href="class_quant_lib_1_1_stochastic_process.html" shape="rect" coords="33,82,175,106" alt="">
<area href="class_quant_lib_1_1_observer.html" shape="rect" coords="5,7,88,31" alt="">
<area href="class_quant_lib_1_1_observable.html" shape="rect" coords="112,7,211,31" alt="">
</map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center><a href="class_quant_lib_1_1_heston_process-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Square-root stochastic-volatility Heston process.
<p>
This class describes the square root stochastic volatility process governed by <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{array}{rcl} dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \end{array} \]" src="form_189.png">
<p>
<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="102e30e7107468e4fb2c1040044e0627"></a><!-- doxytag: member="QuantLib::HestonProcess::HestonProcess" ref="102e30e7107468e4fb2c1040044e0627" args="(const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > &dividendYield, const Handle< Quote > &s0, Real v0, Real kappa, Real theta, Real sigma, Real rho)" -->
</td><td class="memItemRight" valign="bottom"><b>HestonProcess</b> (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> > &riskFreeRate, 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> > &dividendYield, 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> > &s0, Real v0, Real kappa, Real theta, Real sigma, Real rho)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cce0ab2cacc475b2434f24c65c91685a"></a><!-- doxytag: member="QuantLib::HestonProcess::size" ref="cce0ab2cacc475b2434f24c65c91685a" args="() const" -->
Size </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_heston_process.html#cce0ab2cacc475b2434f24c65c91685a">size</a> () const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the number of dimensions of the stochastic process <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="370c708931771eb9459d0ac2db0426ee"></a><!-- doxytag: member="QuantLib::HestonProcess::initialValues" ref="370c708931771eb9459d0ac2db0426ee" args="() const" -->
<a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_array.html">Array</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_heston_process.html#370c708931771eb9459d0ac2db0426ee">initialValues</a> () const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the initial values of the state variables <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9e716cd0b67d0a8183a4ffa4ff394757"></a><!-- doxytag: member="QuantLib::HestonProcess::drift" ref="9e716cd0b67d0a8183a4ffa4ff394757" args="(Time t, const Array &x) const" -->
<a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_array.html">Array</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_heston_process.html#9e716cd0b67d0a8183a4ffa4ff394757">drift</a> (Time t, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x) const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the drift part of the equation, i.e., <img class="formulaInl" alt="$ \mu(t, \mathrm{x}_t) $" src="form_242.png"> <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="00c42da0242ba9ac04b2842dc9f0acd9"></a><!-- doxytag: member="QuantLib::HestonProcess::diffusion" ref="00c42da0242ba9ac04b2842dc9f0acd9" args="(Time t, const Array &x) const" -->
<a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_heston_process.html#00c42da0242ba9ac04b2842dc9f0acd9">diffusion</a> (Time t, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x) const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the diffusion part of the equation, i.e. <img class="formulaInl" alt="$ \sigma(t, \mathrm{x}_t) $" src="form_243.png"> <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_array.html">Array</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_heston_process.html#d16a97eee0ebc79cbf0c11c69d46b490">apply</a> (const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x0, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &dx) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5641dc84f2df4c813ec2b862fb5b2c34"></a><!-- doxytag: member="QuantLib::HestonProcess::s0" ref="5641dc84f2df4c813ec2b862fb5b2c34" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>s0</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8b9537c785da7b6872482fee29cfb731"></a><!-- doxytag: member="QuantLib::HestonProcess::v0" ref="8b9537c785da7b6872482fee29cfb731" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>v0</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="891ea127047dcd9acc1dff3dbf26e88e"></a><!-- doxytag: member="QuantLib::HestonProcess::rho" ref="891ea127047dcd9acc1dff3dbf26e88e" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>rho</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d88e3ab524ca113ef0aed0c85918b1f2"></a><!-- doxytag: member="QuantLib::HestonProcess::kappa" ref="d88e3ab524ca113ef0aed0c85918b1f2" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>kappa</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="211532127d83c15b17647a043e9efd36"></a><!-- doxytag: member="QuantLib::HestonProcess::theta" ref="211532127d83c15b17647a043e9efd36" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>theta</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3bf7456c7feee4fc5c40c1ea775619de"></a><!-- doxytag: member="QuantLib::HestonProcess::sigma" ref="3bf7456c7feee4fc5c40c1ea775619de" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>sigma</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="92c9fee1943b383e94a3c5463b401014"></a><!-- doxytag: member="QuantLib::HestonProcess::dividendYield" ref="92c9fee1943b383e94a3c5463b401014" args="() const" -->
const boost::shared_ptr< <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="433735211cce8cc9f1851fe855546fd0"></a><!-- doxytag: member="QuantLib::HestonProcess::riskFreeRate" ref="433735211cce8cc9f1851fe855546fd0" args="() const" -->
const boost::shared_ptr< <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">Time </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_heston_process.html#f8a1d4ca4369b3009d08291f1c2d7744">time</a> (const <a class="el" href="class_quant_lib_1_1_date.html">Date</a> &) const </td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="d16a97eee0ebc79cbf0c11c69d46b490"></a><!-- doxytag: member="QuantLib::HestonProcess::apply" ref="d16a97eee0ebc79cbf0c11c69d46b490" args="(const Array &x0, const Array &dx) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a><<a class="el" href="class_quant_lib_1_1_array.html">Array</a>> apply </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td>
<td class="paramname"> <em>dx</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
applies a change to the asset value. By default, it returns <img class="formulaInl" alt="$ \mathrm{x} + \Delta \mathrm{x} $" src="form_250.png">.
<p>
Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process.html#2f8f5deb5ff248f45bb56c4054f000ec">StochasticProcess</a>.
</div>
</div><p>
<a class="anchor" name="f8a1d4ca4369b3009d08291f1c2d7744"></a><!-- doxytag: member="QuantLib::HestonProcess::time" ref="f8a1d4ca4369b3009d08291f1c2d7744" args="(const Date &) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">Time 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>
</tr>
</table>
</div>
<div class="memdoc">
<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>.
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