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<h3 class="navbartitle">Version 0.9.7</h3>
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<h3 class="navbartitle">Version 0.9.9</h3>
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<h3 class="navbartitle">Getting started</h3>
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<ul class="navbarlist">
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<li class="navlink"><a href="index.html">Introduction</a></li>
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<li class="navlink"><a href="overview.html">Project overview</a></li>
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<li class="navlink"><a href="where.html">Where to get QuantLib</a></li>
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<li class="navlink"><a href="install.html">Installation</a></li>
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<li class="navlink"><a href="config.html">Configuration</a></li>
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<div class="dynsection">
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<p><center><img src="class_quant_lib_1_1_stochastic_process__inherit__graph.png" border="0" usemap="#_stochastic_process__inherit__map" alt="Inheritance graph"></center>
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<map name="_stochastic_process__inherit__map">
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<area shape="rect" href="class_quant_lib_1_1_forward_measure_process.html" title="forward-measure stochastic process" alt="" coords="329,5,495,32"><area shape="rect" href="class_quant_lib_1_1_g2_process.html" title="G2 stochastic process" alt="" coords="369,56,455,82"><area shape="rect" href="class_quant_lib_1_1_g_j_r_g_a_r_c_h_process.html" title="Stochastic-volatility GJR-GARCH(1,1) process." alt="" coords="341,106,483,133"><area shape="rect" href="class_quant_lib_1_1_heston_process.html" title="Square-root stochastic-volatility Heston process." alt="" coords="357,157,467,184"><area shape="rect" href="class_quant_lib_1_1_libor_forward_model_process.html" title="libor-forward-model process" alt="" coords="323,208,501,234"><area shape="rect" href="class_quant_lib_1_1_stochastic_process1_d.html" title="1-dimensional stochastic process" alt="" coords="339,258,485,285"><area shape="rect" href="class_quant_lib_1_1_stochastic_process_array.html" title="Array of correlated 1-D stochastic processes" alt="" coords="331,309,493,336"><area shape="rect" href="class_quant_lib_1_1_observer.html" title="Object that gets notified when a given observable changes." alt="" coords="12,132,87,158"><area shape="rect" href="class_quant_lib_1_1_observable.html" title="Object that notifies its changes to a set of observables." alt="" coords="5,182,93,209"></map>
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<area shape="rect" href="class_quant_lib_1_1_forward_measure_process.html" title="forward-measure stochastic process" alt="" coords="341,5,507,35"><area shape="rect" href="class_quant_lib_1_1_g2_process.html" title="G2 stochastic process" alt="" coords="381,59,467,88"><area shape="rect" href="class_quant_lib_1_1_g_j_r_g_a_r_c_h_process.html" title="Stochastic-volatility GJR-GARCH(1,1) process." alt="" coords="355,112,493,141"><area shape="rect" href="class_quant_lib_1_1_heston_process.html" title="Square-root stochastic-volatility Heston process." alt="" coords="369,165,479,195"><area shape="rect" href="class_quant_lib_1_1_hybrid_heston_hull_white_process.html" title="Hybrid Heston Hull-White stochastic process." alt="" coords="323,219,525,248"><area shape="rect" href="class_quant_lib_1_1_libor_forward_model_process.html" title="libor-forward-model process" alt="" coords="335,272,513,301"><area shape="rect" href="class_quant_lib_1_1_stochastic_process1_d.html" title="1-dimensional stochastic process" alt="" coords="351,325,497,355"><area shape="rect" href="class_quant_lib_1_1_stochastic_process_array.html" title="Array of correlated 1-D stochastic processes" alt="" coords="343,379,505,408"><area shape="rect" href="class_quant_lib_1_1_observer.html" title="Object that gets notified when a given observable changes." alt="" coords="12,165,87,195"><area shape="rect" href="class_quant_lib_1_1_observable.html" title="Object that notifies its changes to a set of observers." alt="" coords="5,219,93,248"></map>
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<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
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<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="dd74d4d9a1354fee6d3df7662b14e7e1"></a><!-- doxytag: member="QuantLib::StochasticProcess::drift" ref="dd74d4d9a1354fee6d3df7662b14e7e1" args="(Time t, const Array &x) const =0" -->
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virtual <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_stochastic_process.html#dd74d4d9a1354fee6d3df7662b14e7e1">drift</a> (Time t, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x) const =0</td></tr>
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<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) $" src="form_348.png"> <br></td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the drift part of the equation, i.e., <img class="formulaInl" alt="$ \mu(t, \mathrm{x}_t) $" src="form_341.png"> <br></td></tr>
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<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8562aad455e247b42d47aab2b18f205a"></a><!-- doxytag: member="QuantLib::StochasticProcess::diffusion" ref="8562aad455e247b42d47aab2b18f205a" args="(Time t, const Array &x) const =0" -->
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virtual <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process.html#8562aad455e247b42d47aab2b18f205a">diffusion</a> (Time t, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x) const =0</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the diffusion part of the equation, i.e. <img class="formulaInl" alt="$ \sigma(t, \mathrm{x}_t) $" src="form_349.png"> <br></td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the diffusion part of the equation, i.e. <img class="formulaInl" alt="$ \sigma(t, \mathrm{x}_t) $" src="form_342.png"> <br></td></tr>
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<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual <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_stochastic_process.html#90f2fadbc2346fb7f6c94611215a068b">expectation</a> (Time t0, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x0, Time dt) const </td></tr>
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<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual <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_stochastic_process.html#f60142c7a240fe9fa7a9458740815b9c">stdDeviation</a> (Time t0, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x0, Time dt) const </td></tr>
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multi-dimensional stochastic process class.
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This class describes a stochastic process governed by <p class="formulaDsp">
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<img class="formulaDsp" alt="\[ d\mathrm{x}_t = \mu(t, x_t)\mathrm{d}t + \sigma(t, \mathrm{x}_t) \cdot d\mathrm{W}_t. \]" src="form_346.png">
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<img class="formulaDsp" alt="\[ d\mathrm{x}_t = \mu(t, x_t)\mathrm{d}t + \sigma(t, \mathrm{x}_t) \cdot d\mathrm{W}_t. \]" src="form_339.png">
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<hr><h2>Member Function Documentation</h2>
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<a class="anchor" name="90f2fadbc2346fb7f6c94611215a068b"></a><!-- doxytag: member="QuantLib::StochasticProcess::expectation" ref="90f2fadbc2346fb7f6c94611215a068b" args="(Time t0, const Array &x0, Time dt) const " -->
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returns the expectation <img class="formulaInl" alt="$ E(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) $" src="form_350.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_351.png"> according to the given <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>. This method can be overridden in derived classes which want to hard-code a particular <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>.
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returns the expectation <img class="formulaInl" alt="$ E(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) $" src="form_343.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_344.png"> according to the given <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>. This method can be overridden in derived classes which want to hard-code a particular <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>.
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<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_g2_process.html#30a103c583af9320f08337052d38c622">G2Process</a>, <a class="el" href="class_quant_lib_1_1_g2_forward_process.html#30a103c583af9320f08337052d38c622">G2ForwardProcess</a>, and <a class="el" href="class_quant_lib_1_1_stochastic_process_array.html#30a103c583af9320f08337052d38c622">StochasticProcessArray</a>.</p>
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returns the standard deviation <img class="formulaInl" alt="$ S(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) $" src="form_352.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_351.png"> according to the given <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>. This method can be overridden in derived classes which want to hard-code a particular <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>.
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returns the standard deviation <img class="formulaInl" alt="$ S(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) $" src="form_345.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_344.png"> according to the given <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>. This method can be overridden in derived classes which want to hard-code a particular <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>.
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<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_g2_process.html#b55b8ade4729f4509ad40bbaab050a0d">G2Process</a>, <a class="el" href="class_quant_lib_1_1_g2_forward_process.html#b55b8ade4729f4509ad40bbaab050a0d">G2ForwardProcess</a>, and <a class="el" href="class_quant_lib_1_1_stochastic_process_array.html#b55b8ade4729f4509ad40bbaab050a0d">StochasticProcessArray</a>.</p>
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returns the covariance <img class="formulaInl" alt="$ V(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) $" src="form_353.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_351.png"> according to the given <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>. This method can be overridden in derived classes which want to hard-code a particular <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>.
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returns the covariance <img class="formulaInl" alt="$ V(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) $" src="form_346.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_344.png"> according to the given <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>. This method can be overridden in derived classes which want to hard-code a particular <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>.
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<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_libor_forward_model_process.html#a35146549bd167f407791342e89927e3">LiborForwardModelProcess</a>, <a class="el" href="class_quant_lib_1_1_g2_process.html#a35146549bd167f407791342e89927e3">G2Process</a>, <a class="el" href="class_quant_lib_1_1_g2_forward_process.html#a35146549bd167f407791342e89927e3">G2ForwardProcess</a>, and <a class="el" href="class_quant_lib_1_1_stochastic_process_array.html#a35146549bd167f407791342e89927e3">StochasticProcessArray</a>.</p>
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<div class="memdoc">
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returns the asset value after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_351.png"> according to the given <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>. By default, it returns <p class="formulaDsp">
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<img class="formulaDsp" alt="\[ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]" src="form_354.png">
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returns the asset value after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_344.png"> according to the given <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval">discretization</a>. By default, it returns <p class="formulaDsp">
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<img class="formulaDsp" alt="\[ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]" src="form_347.png">
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where <img class="formulaInl" alt="$ E $" src="form_355.png"> is the expectation and <img class="formulaInl" alt="$ S $" src="form_213.png"> the standard deviation.
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<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_libor_forward_model_process.html#89ac97af7698aa193a9c0731dcdd9d8a">LiborForwardModelProcess</a>, <a class="el" href="class_quant_lib_1_1_bates_process.html#89ac97af7698aa193a9c0731dcdd9d8a">BatesProcess</a>, <a class="el" href="class_quant_lib_1_1_g_j_r_g_a_r_c_h_process.html#89ac97af7698aa193a9c0731dcdd9d8a">GJRGARCHProcess</a>, <a class="el" href="class_quant_lib_1_1_heston_process.html#89ac97af7698aa193a9c0731dcdd9d8a">HestonProcess</a>, and <a class="el" href="class_quant_lib_1_1_stochastic_process_array.html#89ac97af7698aa193a9c0731dcdd9d8a">StochasticProcessArray</a>.</p>
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where <img class="formulaInl" alt="$ E $" src="form_348.png"> is the expectation and <img class="formulaInl" alt="$ S $" src="form_202.png"> the standard deviation.
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<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_libor_forward_model_process.html#89ac97af7698aa193a9c0731dcdd9d8a">LiborForwardModelProcess</a>, <a class="el" href="class_quant_lib_1_1_bates_process.html#89ac97af7698aa193a9c0731dcdd9d8a">BatesProcess</a>, <a class="el" href="class_quant_lib_1_1_g_j_r_g_a_r_c_h_process.html#89ac97af7698aa193a9c0731dcdd9d8a">GJRGARCHProcess</a>, <a class="el" href="class_quant_lib_1_1_heston_process.html#89ac97af7698aa193a9c0731dcdd9d8a">HestonProcess</a>, <a class="el" href="class_quant_lib_1_1_hybrid_heston_hull_white_process.html#89ac97af7698aa193a9c0731dcdd9d8a">HybridHestonHullWhiteProcess</a>, and <a class="el" href="class_quant_lib_1_1_stochastic_process_array.html#89ac97af7698aa193a9c0731dcdd9d8a">StochasticProcessArray</a>.</p>
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applies a change to the asset value. By default, it returns <img class="formulaInl" alt="$ \mathrm{x} + \Delta \mathrm{x} $" src="form_356.png">.
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<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_libor_forward_model_process.html#87d025fa8e0daa4e048320c7ac266bb3">LiborForwardModelProcess</a>, <a class="el" href="class_quant_lib_1_1_g_j_r_g_a_r_c_h_process.html#87d025fa8e0daa4e048320c7ac266bb3">GJRGARCHProcess</a>, <a class="el" href="class_quant_lib_1_1_heston_process.html#87d025fa8e0daa4e048320c7ac266bb3">HestonProcess</a>, and <a class="el" href="class_quant_lib_1_1_stochastic_process_array.html#87d025fa8e0daa4e048320c7ac266bb3">StochasticProcessArray</a>.</p>
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applies a change to the asset value. By default, it returns <img class="formulaInl" alt="$ \mathrm{x} + \Delta \mathrm{x} $" src="form_349.png">.
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<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_libor_forward_model_process.html#87d025fa8e0daa4e048320c7ac266bb3">LiborForwardModelProcess</a>, <a class="el" href="class_quant_lib_1_1_g_j_r_g_a_r_c_h_process.html#87d025fa8e0daa4e048320c7ac266bb3">GJRGARCHProcess</a>, <a class="el" href="class_quant_lib_1_1_heston_process.html#87d025fa8e0daa4e048320c7ac266bb3">HestonProcess</a>, <a class="el" href="class_quant_lib_1_1_hybrid_heston_hull_white_process.html#87d025fa8e0daa4e048320c7ac266bb3">HybridHestonHullWhiteProcess</a>, and <a class="el" href="class_quant_lib_1_1_stochastic_process_array.html#87d025fa8e0daa4e048320c7ac266bb3">StochasticProcessArray</a>.</p>
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returns the time value corresponding to the given date in the reference system of the stochastic process.<p>
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<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>
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<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#f8a1d4ca4369b3009d08291f1c2d7744">GeneralizedBlackScholesProcess</a>, <a class="el" href="class_quant_lib_1_1_g_j_r_g_a_r_c_h_process.html#f8a1d4ca4369b3009d08291f1c2d7744">GJRGARCHProcess</a>, <a class="el" href="class_quant_lib_1_1_heston_process.html#f8a1d4ca4369b3009d08291f1c2d7744">HestonProcess</a>, <a class="el" href="class_quant_lib_1_1_merton76_process.html#f8a1d4ca4369b3009d08291f1c2d7744">Merton76Process</a>, and <a class="el" href="class_quant_lib_1_1_stochastic_process_array.html#f8a1d4ca4369b3009d08291f1c2d7744">StochasticProcessArray</a>.</p>
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<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#f8a1d4ca4369b3009d08291f1c2d7744">GeneralizedBlackScholesProcess</a>, <a class="el" href="class_quant_lib_1_1_g_j_r_g_a_r_c_h_process.html#f8a1d4ca4369b3009d08291f1c2d7744">GJRGARCHProcess</a>, <a class="el" href="class_quant_lib_1_1_heston_process.html#f8a1d4ca4369b3009d08291f1c2d7744">HestonProcess</a>, <a class="el" href="class_quant_lib_1_1_hybrid_heston_hull_white_process.html#748380f774765c5190c570c0c8a8091e">HybridHestonHullWhiteProcess</a>, <a class="el" href="class_quant_lib_1_1_merton76_process.html#f8a1d4ca4369b3009d08291f1c2d7744">Merton76Process</a>, and <a class="el" href="class_quant_lib_1_1_stochastic_process_array.html#f8a1d4ca4369b3009d08291f1c2d7744">StochasticProcessArray</a>.</p>
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