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<h3 class="subtitle">A free/open-source library for quantitative finance</h3>
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<li class="navelem"><b>QuantLib</b> </li>
<li class="navelem"><a class="el" href="class_quant_lib_1_1_bates_engine.html">BatesEngine</a> </li>
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<a href="#pub-methods">Public Member Functions</a> |
<a href="#pro-methods">Protected Member Functions</a> </div>
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<div class="title">BatesEngine Class Reference<div class="ingroups"><a class="el" href="group__vanillaengines.html">Vanilla option engines</a></div></div> </div>
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<!-- doxytag: class="QuantLib::BatesEngine" --><!-- doxytag: inherits="QuantLib::AnalyticHestonEngine" -->
<p>Bates model engines based on Fourier transform.
<a href="class_quant_lib_1_1_bates_engine.html#details">More...</a></p>
<p><code>#include <ql/pricingengines/vanilla/batesengine.hpp></code></p>
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Inheritance diagram for BatesEngine:</div>
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Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a612699f44f77c40d5705fa99c68934d7"></a><!-- doxytag: member="QuantLib::BatesEngine::BatesEngine" ref="a612699f44f77c40d5705fa99c68934d7" args="(const boost::shared_ptr< BatesModel > &model, Size integrationOrder=144)" -->
 </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, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> integrationOrder=144)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a853de5b5181bc1c9ca97e2c89574db02"></a><!-- doxytag: member="QuantLib::BatesEngine::BatesEngine" ref="a853de5b5181bc1c9ca97e2c89574db02" args="(const boost::shared_ptr< BatesModel > &model, Real relTolerance, Size maxEvaluations)" -->
 </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, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> relTolerance, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> maxEvaluations)</td></tr>
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Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aa10b245f3027db04aabb719f95dae0c6"></a><!-- doxytag: member="QuantLib::BatesEngine::addOnTerm" ref="aa10b245f3027db04aabb719f95dae0c6" args="(Real phi, Time t, Size j) const " -->
std::complex< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > </td><td class="memItemRight" valign="bottom"><b>addOnTerm</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> phi, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> j) const </td></tr>
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<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Bates model engines based on Fourier transform. </p>
<p>this classes price european options under the following processes</p>
<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_322.png"/>
</p>
<p>N is a Poisson process with the intensity <img class="formulaInl" alt="$ \lambda $" src="form_29.png"/>. When a jump occurs the magnitude J has the probability density function <img class="formulaInl" alt="$ \omega(J) $" src="form_323.png"/>.</p>
<p>1.1 Log-Normal Jump Diffusion: <a class="el" href="class_quant_lib_1_1_bates_engine.html" title="Bates model engines based on Fourier transform.">BatesEngine</a></p>
<p>Logarithm of the jump size J is normally distributed </p>
<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_324.png"/>
</p>
<p>1.2 Double-Exponential Jump Diffusion: BatesDoubleExpEngine</p>
<p>The jump size has an asymmetric double exponential distribution </p>
<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_325.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_326.png"/>
</p>
<p>2.1 Log-Normal Jump Diffusion with Deterministic Jump Intensity BatesDetJumpEngine</p>
<p>2.2 Double-Exponential Jump Diffusion with Deterministic Jump Intensity BatesDoubleExpDetJumpEngine</p>
<p>References:</p>
<p>D. Bates, Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options, Review of Financial Sudies 9, 69-107.</p>
<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 class="test"><dt><b><a class="el" href="test.html#_test000119">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>
<dl><dt><b>Examples: </b></dt><dd><a class="el" href="_equity_option_8cpp-example.html#_a32">EquityOption.cpp</a>.</dd>
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