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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_bates_engine.html">BatesEngine</a></div>
<h1>BatesEngine Class Reference<br>
<small>
[<a class="el" href="group__vanillaengines.html">Vanilla option engines</a>]</small>
</h1><!-- doxytag: class="QuantLib::BatesEngine" --><!-- doxytag: inherits="QuantLib::AnalyticHestonEngine" --><code>#include <ql/PricingEngines/Vanilla/batesengine.hpp></code>
<p>
Inheritance diagram for BatesEngine:<p><center><img src="class_quant_lib_1_1_bates_engine__inherit__graph.png" border="0" usemap="#_bates_engine__inherit__map" alt="Inheritance graph"></center>
<map name="_bates_engine__inherit__map">
<area href="class_quant_lib_1_1_analytic_heston_engine.html" shape="rect" coords="261,306,432,330" alt="">
<area href="class_quant_lib_1_1_generic_model_engine.html" shape="rect" coords="5,231,688,255" alt="">
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<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center><a href="class_quant_lib_1_1_bates_engine-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Bates model engines based on Fourier transform.
<p>
this classes price european options under the following processes<p>
1. Jump-Diffusion with Stochastic Volatility<p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \end{array} \]" src="form_173.png">
<p>
<p>
N is a Poisson process with the intensity <img class="formulaInl" alt="$ \lambda $" src="form_29.png">. When a jump occurs the magnitude J has the probability distribution function <img class="formulaInl" alt="$ \omega(J) $" src="form_174.png">.<p>
1.1 Log-Normal Jump Diffusion: <a class="el" href="class_quant_lib_1_1_bates_engine.html">BatesEngine</a><p>
Logarithm of the jump size J is normally distributed <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \omega(J) = \frac{1}{\sqrt{2\pi \delta^2}} \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right] \]" src="form_175.png">
<p>
<p>
1.2 Double-Exponential Jump Diffusion: BatesDoubleExpEngine<p>
The jump size has an asymmetric double exponential distribution <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{array}{rcl} \omega(J)&=& p\frac{1}{\eta_u}e^{-\frac{1}{\eta_u}J} 1_{J>0} + q\frac{1}{\eta_d}e^{\frac{1}{\eta_d}J} 1_{J<0} \\ p + q &=& 1 \end{array} \]" src="form_176.png">
<p>
<p>
2. Stochastic Volatility with Jump Diffusion and Deterministic Jump Intensity<p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ d\lambda(t) &=& \kappa_\lambda(\theta_\lambda-\lambda) dt \\ dW_1 dW_2 &=& \rho dt \end{array} \]" src="form_177.png">
<p>
<p>
2.1 Log-Normal Jump Diffusion with Deterministic Jump Intensity BatesDetJumpEngine<p>
2.2 Double-Exponential Jump Diffusion with Deterministic Jump Intensity BatesDoubleExpDetJumpEngine<p>
References:<p>
D. Bates, Jumps and stochastic volatilit: exchange rate processes implicit in Deutsche mark options", Review of Financial Sudies 9, 69-107.<p>
A. Sepp, Pricing European-Style Options under Jump Diffusion Processes with Stochastic Volatility: Applications of Fourier Transform (<<a href="http://math.ut.ee/~spartak/papers/stochjumpvols.pdf">http://math.ut.ee/~spartak/papers/stochjumpvols.pdf</a>>)<p>
<dl compact><dt><b><a class="el" href="test.html#_test000086">Tests:</a></b></dt><dd>the correctness of the returned value is tested by reproducing results available in web/literature, testing against QuantLib's jump diffusion engine and comparison with Black pricing. </dd></dl>
<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="bbae95e685f13ab1df9dc52335ff58c9"></a><!-- doxytag: member="QuantLib::BatesEngine::BatesEngine" ref="bbae95e685f13ab1df9dc52335ff58c9" args="(const boost::shared_ptr< BatesModel > &model, Size integrationOrder=64)" -->
</td><td class="memItemRight" valign="bottom"><b>BatesEngine</b> (const boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_bates_model.html">BatesModel</a> > &model, Size integrationOrder=64)</td></tr>
<tr><td colspan="2"><br><h2>Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="dbd1ee43670acd37cd35d25c7e057bf0"></a><!-- doxytag: member="QuantLib::BatesEngine::jumpDiffusionTerm" ref="dbd1ee43670acd37cd35d25c7e057bf0" args="(Real phi, Time t, Size j) const" -->
std::complex< Real > </td><td class="memItemRight" valign="bottom"><b>jumpDiffusionTerm</b> (Real phi, Time t, Size j) const</td></tr>
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