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<li class="navelem"><a class="el" href="namespace_quant_lib.html">QuantLib</a></li><li class="navelem"><a class="el" href="class_quant_lib_1_1_heston_process.html">HestonProcess</a></li> </ul>
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<div class="title">HestonProcess Class Reference<div class="ingroups"><a class="el" href="group__processes.html">Stochastic processes</a></div></div> </div>
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<p>Square-root stochastic-volatility Heston process.
<a href="class_quant_lib_1_1_heston_process.html#details">More...</a></p>
<p><code>#include <ql/processes/hestonprocess.hpp></code></p>
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for HestonProcess:</div>
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<area shape="rect" title="Square-root stochastic-volatility Heston process." alt="" coords="39,155,151,181"/>
<area shape="rect" href="class_quant_lib_1_1_bates_process.html" title="Square-root stochastic-volatility Bates process." alt="" coords="43,229,147,256"/>
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<table class="memberdecls">
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Public Types</h2></td></tr>
<tr class="memitem:a36f45ac51e3e98d35c68ca85b7573e87"><td class="memItemLeft" align="right" valign="top"><a id="a36f45ac51e3e98d35c68ca85b7573e87"></a>enum  </td><td class="memItemRight" valign="bottom"><b>Discretization</b> { <br />
  <b>PartialTruncation</b>,
<b>FullTruncation</b>,
<b>Reflection</b>,
<b>NonCentralChiSquareVariance</b>,
<br />
  <b>QuadraticExponential</b>,
<b>QuadraticExponentialMartingale</b>,
<b>BroadieKayaExactSchemeLobatto</b>,
<b>BroadieKayaExactSchemeLaguerre</b>,
<br />
  <b>BroadieKayaExactSchemeTrapezoidal</b>
<br />
}</td></tr>
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typedef boost::unordered_set< ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> > > </td><td class="memItemRight" valign="bottom"><b>set_type</b></td></tr>
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typedef set_type::iterator </td><td class="memItemRight" valign="bottom"><b>iterator</b></td></tr>
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Public Member Functions</h2></td></tr>
<tr class="memitem:a1c870156ecd22adb2873f0a3a43099e6"><td class="memItemLeft" align="right" valign="top"><a id="a1c870156ecd22adb2873f0a3a43099e6"></a>
 </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, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> v0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> kappa, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> theta, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> sigma, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> rho, Discretization d=QuadraticExponentialMartingale)</td></tr>
<tr class="separator:a1c870156ecd22adb2873f0a3a43099e6"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acce0ab2cacc475b2434f24c65c91685a"><td class="memItemLeft" align="right" valign="top"><a id="acce0ab2cacc475b2434f24c65c91685a"></a>
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_heston_process.html#acce0ab2cacc475b2434f24c65c91685a">size</a> () const</td></tr>
<tr class="memdesc:acce0ab2cacc475b2434f24c65c91685a"><td class="mdescLeft"> </td><td class="mdescRight">returns the number of dimensions of the stochastic process <br /></td></tr>
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<tr class="memitem:a80d7c2dfc8a2fa937425f38ce5cacd41"><td class="memItemLeft" align="right" valign="top"><a id="a80d7c2dfc8a2fa937425f38ce5cacd41"></a>
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_heston_process.html#a80d7c2dfc8a2fa937425f38ce5cacd41">factors</a> () const</td></tr>
<tr class="memdesc:a80d7c2dfc8a2fa937425f38ce5cacd41"><td class="mdescLeft"> </td><td class="mdescRight">returns the number of independent factors of the process <br /></td></tr>
<tr class="separator:a80d7c2dfc8a2fa937425f38ce5cacd41"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a370c708931771eb9459d0ac2db0426ee"><td class="memItemLeft" align="right" valign="top"><a id="a370c708931771eb9459d0ac2db0426ee"></a>
<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#a370c708931771eb9459d0ac2db0426ee">initialValues</a> () const</td></tr>
<tr class="memdesc:a370c708931771eb9459d0ac2db0426ee"><td class="mdescLeft"> </td><td class="mdescRight">returns the initial values of the state variables <br /></td></tr>
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<tr class="memitem:a9e716cd0b67d0a8183a4ffa4ff394757"><td class="memItemLeft" align="right" valign="top"><a id="a9e716cd0b67d0a8183a4ffa4ff394757"></a>
<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#a9e716cd0b67d0a8183a4ffa4ff394757">drift</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x) const</td></tr>
<tr class="memdesc:a9e716cd0b67d0a8183a4ffa4ff394757"><td class="mdescLeft"> </td><td class="mdescRight">returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \) <br /></td></tr>
<tr class="separator:a9e716cd0b67d0a8183a4ffa4ff394757"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a00c42da0242ba9ac04b2842dc9f0acd9"><td class="memItemLeft" align="right" valign="top"><a id="a00c42da0242ba9ac04b2842dc9f0acd9"></a>
<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#a00c42da0242ba9ac04b2842dc9f0acd9">diffusion</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x) const</td></tr>
<tr class="memdesc:a00c42da0242ba9ac04b2842dc9f0acd9"><td class="mdescLeft"> </td><td class="mdescRight">returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \) <br /></td></tr>
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<tr class="memitem:ad16a97eee0ebc79cbf0c11c69d46b490"><td class="memItemLeft" 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#ad16a97eee0ebc79cbf0c11c69d46b490">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>
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<tr class="memitem:af32a2b7d3aa8ec2addf422ed1b15a525"><td class="memItemLeft" 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#af32a2b7d3aa8ec2addf422ed1b15a525">evolve</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x0, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &dw) const</td></tr>
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<tr class="memitem:a8b9537c785da7b6872482fee29cfb731"><td class="memItemLeft" align="right" valign="top"><a id="a8b9537c785da7b6872482fee29cfb731"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>v0</b> () const</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>rho</b> () const</td></tr>
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<tr class="memitem:ad88e3ab524ca113ef0aed0c85918b1f2"><td class="memItemLeft" align="right" valign="top"><a id="ad88e3ab524ca113ef0aed0c85918b1f2"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>kappa</b> () const</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>theta</b> () const</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>sigma</b> () const</td></tr>
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<tr class="memitem:ae46113b213d8d15f37dc9f00e685a0b8"><td class="memItemLeft" align="right" valign="top"><a id="ae46113b213d8d15f37dc9f00e685a0b8"></a>
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>
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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> > & </td><td class="memItemRight" valign="bottom"><b>dividendYield</b> () const</td></tr>
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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> > & </td><td class="memItemRight" valign="bottom"><b>riskFreeRate</b> () const</td></tr>
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<tr class="memitem:ab2e3e42e764f5a50686da1cb9ea153be"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_heston_process.html#ab2e3e42e764f5a50686da1cb9ea153be">time</a> (const <a class="el" href="class_quant_lib_1_1_date.html">Date</a> &) const</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>pdf</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> v, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> eps=1e-3) const</td></tr>
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<tr class="inherit_header pub_methods_class_quant_lib_1_1_stochastic_process"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_stochastic_process')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_stochastic_process.html">StochasticProcess</a></td></tr>
<tr class="memitem:a5ff82c7ea229ea678252bca22f1ee455 inherit pub_methods_class_quant_lib_1_1_stochastic_process"><td class="memItemLeft" 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#a5ff82c7ea229ea678252bca22f1ee455">expectation</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x0, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const</td></tr>
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<tr class="memitem:a1d143e05259160f677407c6cb3b7d8b4 inherit pub_methods_class_quant_lib_1_1_stochastic_process"><td class="memItemLeft" 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#a1d143e05259160f677407c6cb3b7d8b4">stdDeviation</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x0, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const</td></tr>
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<tr class="memitem:a7d7d88e8f05305804aed59a6521f8a36 inherit pub_methods_class_quant_lib_1_1_stochastic_process"><td class="memItemLeft" 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#a7d7d88e8f05305804aed59a6521f8a36">covariance</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x0, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const</td></tr>
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<tr class="memitem:ac5c54df7ed3b930268c8d7752c101725 inherit pub_methods_class_quant_lib_1_1_stochastic_process"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process.html#ac5c54df7ed3b930268c8d7752c101725">update</a> ()</td></tr>
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<tr class="inherit_header pub_methods_class_quant_lib_1_1_observer"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_observer')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_observer.html">Observer</a></td></tr>
<tr class="memitem:af6a9d3ca0b7f388f3b7ccb1eccf11f63 inherit pub_methods_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top"><a id="af6a9d3ca0b7f388f3b7ccb1eccf11f63"></a>
 </td><td class="memItemRight" valign="bottom"><b>Observer</b> (const <a class="el" href="class_quant_lib_1_1_observer.html">Observer</a> &)</td></tr>
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<a class="el" href="class_quant_lib_1_1_observer.html">Observer</a> & </td><td class="memItemRight" valign="bottom"><b>operator=</b> (const <a class="el" href="class_quant_lib_1_1_observer.html">Observer</a> &)</td></tr>
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std::pair< iterator, bool > </td><td class="memItemRight" valign="bottom"><b>registerWith</b> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> > &)</td></tr>
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<tr class="memitem:a51d57eb97a3a57312a47bda29235f182 inherit pub_methods_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_observer.html#a51d57eb97a3a57312a47bda29235f182">registerWithObservables</a> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_observer.html">Observer</a> > &)</td></tr>
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<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>unregisterWith</b> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> > &)</td></tr>
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void </td><td class="memItemRight" valign="bottom"><b>unregisterWithAll</b> ()</td></tr>
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<tr class="memitem:a3d53f9669c128dadc74a5d044a7c8e68 inherit pub_methods_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_observer.html#a3d53f9669c128dadc74a5d044a7c8e68">deepUpdate</a> ()</td></tr>
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<tr class="inherit_header pub_methods_class_quant_lib_1_1_observable"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_observable')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a></td></tr>
<tr class="memitem:a840dd96e33a304cbf681d357de7f48d0 inherit pub_methods_class_quant_lib_1_1_observable"><td class="memItemLeft" align="right" valign="top"><a id="a840dd96e33a304cbf681d357de7f48d0"></a>
 </td><td class="memItemRight" valign="bottom"><b>Observable</b> (const <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> &)</td></tr>
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<tr class="memitem:a522aacdd0f2408fe5e46527a6db999b4 inherit pub_methods_class_quant_lib_1_1_observable"><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_observable.html#a522aacdd0f2408fe5e46527a6db999b4">operator=</a> (const <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> &)</td></tr>
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<tr class="memitem:a397546715bfc5aedd1d16dd202a19d4c inherit pub_methods_class_quant_lib_1_1_observable"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_observable.html#a397546715bfc5aedd1d16dd202a19d4c">notifyObservers</a> ()</td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="inherited"></a>
Additional Inherited Members</h2></td></tr>
<tr class="inherit_header pro_methods_class_quant_lib_1_1_stochastic_process"><td colspan="2" onclick="javascript:toggleInherit('pro_methods_class_quant_lib_1_1_stochastic_process')"><img src="closed.png" alt="-"/> Protected Member Functions inherited from <a class="el" href="class_quant_lib_1_1_stochastic_process.html">StochasticProcess</a></td></tr>
<tr class="memitem:afbd1bbfbbd50f17d99fa61f74dc16437 inherit pro_methods_class_quant_lib_1_1_stochastic_process"><td class="memItemLeft" align="right" valign="top"><a id="afbd1bbfbbd50f17d99fa61f74dc16437"></a>
 </td><td class="memItemRight" valign="bottom"><b>StochasticProcess</b> ()</td></tr>
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<tr class="memitem:a84749d046d61db59992e49b8a7940bc5 inherit pro_methods_class_quant_lib_1_1_stochastic_process"><td class="memItemLeft" align="right" valign="top"><a id="a84749d046d61db59992e49b8a7940bc5"></a>
 </td><td class="memItemRight" valign="bottom"><b>StochasticProcess</b> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">discretization</a> > &)</td></tr>
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<tr class="memitem:a51a940500df8f947d270aaab06f53371 inherit pro_attribs_class_quant_lib_1_1_stochastic_process"><td class="memItemLeft" align="right" valign="top"><a id="a51a940500df8f947d270aaab06f53371"></a>
ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">discretization</a> > </td><td class="memItemRight" valign="bottom"><b>discretization_</b></td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Square-root stochastic-volatility Heston process. </p>
<p>This class describes the square root stochastic volatility process governed by </p><p class="formulaDsp">
\[ \begin{array}{rcl} dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \end{array} \]
</p>
<dl class="section examples"><dt>Examples</dt><dd><a class="el" href="_equity_option_8cpp-example.html#_a27">EquityOption.cpp</a>.</dd>
</dl>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a id="ad16a97eee0ebc79cbf0c11c69d46b490"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad16a97eee0ebc79cbf0c11c69d46b490">◆ </a></span>apply()</h2>
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<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>
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<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td>
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<p>applies a change to the asset value. By default, it returns \( \mathrm{x} + \Delta \mathrm{x} \). </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process.html#a2f8f5deb5ff248f45bb56c4054f000ec">StochasticProcess</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#af32a2b7d3aa8ec2addf422ed1b15a525">◆ </a></span>evolve()</h2>
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<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>> evolve </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>t0</em>, </td>
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<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td>
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<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>dt</em>, </td>
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<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td>
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<td>)</td>
<td></td><td> const</td>
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<p>returns the asset value after a time interval \( \Delta t \) according to the given discretization. By default, it returns </p><p class="formulaDsp">
\[ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]
</p>
<p> where \( E \) is the expectation and \( S \) the standard deviation. </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process.html#a37b5aebef2d35194c059d21a9a793b9c">StochasticProcess</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ab2e3e42e764f5a50686da1cb9ea153be">◆ </a></span>time()</h2>
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<td class="memname"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">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> const</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="section note"><dt>Note</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#a077542ff55ad755add55e8e5e8172cca">StochasticProcess</a>.</p>
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