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<!-- doxytag: class="QuantLib::BatesProcess" --><!-- doxytag: inherits="QuantLib::HestonProcess" -->
<p>Square-root stochastic-volatility Bates process.
<a href="class_quant_lib_1_1_bates_process.html#details">More...</a></p>
<p><code>#include <ql/processes/batesprocess.hpp></code></p>
<div class="dynheader">
Inheritance diagram for BatesProcess:</div>
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<area shape="rect" id="node2" href="class_quant_lib_1_1_heston_process.html" title="Square-root stochastic-volatility Heston process." alt="" coords="5,6,115,37"/></map>
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<p><a href="class_quant_lib_1_1_bates_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="aa53ab896db19eca97e8e53bb62b3d29e"></a><!-- doxytag: member="QuantLib::BatesProcess::BatesProcess" ref="aa53ab896db19eca97e8e53bb62b3d29e" args="(const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > &dividendYield, const Handle< Quote > &s0, Real v0, Real kappa, Real theta, Real sigma, Real rho, Real lambda, Real nu, Real delta, HestonProcess::Discretization d=HestonProcess::FullTruncation)" -->
 </td><td class="memItemRight" valign="bottom"><b>BatesProcess</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, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> lambda, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> nu, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> delta, HestonProcess::Discretization d=HestonProcess::FullTruncation)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="af712ecab6d5754978fed3860efc7f661"></a><!-- doxytag: member="QuantLib::BatesProcess::factors" ref="af712ecab6d5754978fed3860efc7f661" args="() const " -->
<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_bates_process.html#af712ecab6d5754978fed3860efc7f661">factors</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the number of independent factors of the process <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="af971c27bf35db18d8e7e7374e7cf234c"></a><!-- doxytag: member="QuantLib::BatesProcess::drift" ref="af971c27bf35db18d8e7e7374e7cf234c" 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_bates_process.html#af971c27bf35db18d8e7e7374e7cf234c">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><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_351.png"/> <br/></td></tr>
<tr><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_bates_process.html#a89ac97af7698aa193a9c0731dcdd9d8a">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>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a24cb1182953e872918829ca60b348e54"></a><!-- doxytag: member="QuantLib::BatesProcess::lambda" ref="a24cb1182953e872918829ca60b348e54" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>lambda</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a69c12ede1099bb0263342867dd12e045"></a><!-- doxytag: member="QuantLib::BatesProcess::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="a2397bf69d6801e3328c9273143c87ce6"></a><!-- doxytag: member="QuantLib::BatesProcess::delta" ref="a2397bf69d6801e3328c9273143c87ce6" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>delta</b> () const </td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Square-root stochastic-volatility Bates process. </p>
<p>This class describes the square root stochastic volatility process incl jumps governed by </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \\ \omega(J) &=& \frac{1}{\sqrt{2\pi \delta^2}} \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right] \end{array} \]" src="form_327.png"/>
</p>
<dl><dt><b>Examples: </b></dt><dd><a class="el" href="_equity_option_8cpp-example.html#_a30">EquityOption.cpp</a>.</dd>
</dl></div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a89ac97af7698aa193a9c0731dcdd9d8a"></a><!-- doxytag: member="QuantLib::BatesProcess::evolve" ref="a89ac97af7698aa193a9c0731dcdd9d8a" args="(Time t0, const Array &x0, Time dt, const Array &dw) 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>> <a class="el" href="class_quant_lib_1_1_bates_process.html#a89ac97af7698aa193a9c0731dcdd9d8a">evolve</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>t0</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>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>dt</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>dw</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [virtual]</code></td>
</tr>
</table>
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<div class="memdoc">
<p>returns the asset value after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_354.png"/> according to the given discretization. By default, it returns </p>
<p class="formulaDsp">
<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_357.png"/>
</p>
<p> where <img class="formulaInl" alt="$ E $" src="form_358.png"/> is the expectation and <img class="formulaInl" alt="$ S $" src="form_212.png"/> the standard deviation. </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_heston_process.html#a89ac97af7698aa193a9c0731dcdd9d8a">HestonProcess</a>.</p>
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