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<!-- doxytag: class="QuantLib::VarianceGammaProcess" --><!-- doxytag: inherits="QuantLib::StochasticProcess1D" -->
<p>Variance gamma process.
<a href="class_quant_lib_1_1_variance_gamma_process.html#details">More...</a></p>
<p><code>#include <ql/experimental/variancegamma/variancegammaprocess.hpp></code></p>
<div class="dynheader">
Inheritance diagram for VarianceGammaProcess:</div>
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<div class="center"><img src="class_quant_lib_1_1_variance_gamma_process__inherit__graph.png" border="0" usemap="#_variance_gamma_process_inherit__map" alt="Inheritance graph"/></div>
<map name="_variance_gamma_process_inherit__map" id="_variance_gamma_process_inherit__map">
<area shape="rect" id="node2" href="class_quant_lib_1_1_stochastic_process1_d.html" title="1-dimensional stochastic process" alt="" coords="15,6,161,37"/></map>
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<p><a href="class_quant_lib_1_1_variance_gamma_process-members.html">List of all members.</a></p>
<table class="memberdecls">
<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="aedd0446a44f48ee92068daf14f6a8b56"></a><!-- doxytag: member="QuantLib::VarianceGammaProcess::VarianceGammaProcess" ref="aedd0446a44f48ee92068daf14f6a8b56" args="(const Handle< Quote > &s0, const Handle< YieldTermStructure > &dividendYield, const Handle< YieldTermStructure > &riskFreeRate, Real sigma, Real nu, Real theta)" -->
 </td><td class="memItemRight" valign="bottom"><b>VarianceGammaProcess</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> > &s0, 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_yield_term_structure.html">YieldTermStructure</a> > &riskFreeRate, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> sigma, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> nu, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> theta)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a89d2f497b5fd0d0a0dce2ec82c86e778"></a><!-- doxytag: member="QuantLib::VarianceGammaProcess::x0" ref="a89d2f497b5fd0d0a0dce2ec82c86e778" args="() const " -->
<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_variance_gamma_process.html#a89d2f497b5fd0d0a0dce2ec82c86e778">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" align="right" valign="top"><a class="anchor" id="a545d33724b1d6d312eb8a17f73571842"></a><!-- doxytag: member="QuantLib::VarianceGammaProcess::drift" ref="a545d33724b1d6d312eb8a17f73571842" args="(Time t, Real x) const " -->
<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_variance_gamma_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="mdescLeft"> </td><td class="mdescRight">returns the drift part of the equation, i.e. <img class="formulaInl" alt="$ \mu(t, x_t) $" src="form_360.png"/> <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ab4d7fe4af7a6dd0ae710c073569821e4"></a><!-- doxytag: member="QuantLib::VarianceGammaProcess::diffusion" ref="ab4d7fe4af7a6dd0ae710c073569821e4" args="(Time t, Real x) const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_variance_gamma_process.html#ab4d7fe4af7a6dd0ae710c073569821e4">diffusion</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the diffusion part of the equation, i.e. <img class="formulaInl" alt="$ \sigma(t, x_t) $" src="form_361.png"/> <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a78bca11664a7d403bde6a9842f72ae61"></a><!-- doxytag: member="QuantLib::VarianceGammaProcess::sigma" ref="a78bca11664a7d403bde6a9842f72ae61" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>sigma</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a69c12ede1099bb0263342867dd12e045"></a><!-- doxytag: member="QuantLib::VarianceGammaProcess::nu" ref="a69c12ede1099bb0263342867dd12e045" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>nu</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a7a00901daf5bbc66f00e4772cbe0c98f"></a><!-- doxytag: member="QuantLib::VarianceGammaProcess::theta" ref="a7a00901daf5bbc66f00e4772cbe0c98f" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>theta</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a5454c7c9728f2ccef70ac7c9cc0fccee"></a><!-- doxytag: member="QuantLib::VarianceGammaProcess::s0" ref="a5454c7c9728f2ccef70ac7c9cc0fccee" 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>s0</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ad410a408dd37b79578b370b5219dbf80"></a><!-- doxytag: member="QuantLib::VarianceGammaProcess::dividendYield" ref="ad410a408dd37b79578b370b5219dbf80" args="() const " -->
const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a><br class="typebreak"/>
< <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" align="right" valign="top"><a class="anchor" id="a925fdf9de4dd73519b36f975bc7917a8"></a><!-- doxytag: member="QuantLib::VarianceGammaProcess::riskFreeRate" ref="a925fdf9de4dd73519b36f975bc7917a8" args="() const " -->
const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a><br class="typebreak"/>
< <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>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Variance gamma process. </p>
<p>This class describes the stochastic volatility process. With a Brownian motion given by </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ db = \theta dt + \sigma dW_t \]" src="form_142.png"/>
</p>
<p> then a Variance Gamma process X is defined by evaluating this Brownian motion at sample times driven by a Gamma process. If T is the value of a Gamma process with mean 1 and variance rate <img class="formulaInl" alt="$ \nu $" src="form_126.png"/> then the Variance Gamma process is given by </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ X(t) = B(T) \]" src="form_143.png"/>
</p>
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