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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_analytic_heston_engine.html">AnalyticHestonEngine</a></li> </ul>
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<a href="#pub-types">Public Types</a> |
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<div class="title">AnalyticHestonEngine Class Reference<div class="ingroups"><a class="el" href="group__engines.html">Pricing engines</a> » <a class="el" href="group__vanillaengines.html">Vanilla option engines</a></div></div> </div>
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<p>analytic Heston-model engine based on Fourier transform
<a href="class_quant_lib_1_1_analytic_heston_engine.html#details">More...</a></p>
<p><code>#include <ql/pricingengines/vanilla/analytichestonengine.hpp></code></p>
<div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for AnalyticHestonEngine:</div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr class="memitem:a3caae3180358d7e623bcf2dc25e5b627"><td class="memItemLeft" align="right" valign="top"><a id="a3caae3180358d7e623bcf2dc25e5b627"></a>enum  </td><td class="memItemRight" valign="bottom"><b>ComplexLogFormula</b> { <br />
  <b>Gatheral</b>,
<b>BranchCorrection</b>,
<b>AndersenPiterbarg</b>,
<b>AndersenPiterbargOptCV</b>,
<br />
  <b>AsymptoticChF</b>,
<b>OptimalCV</b>
<br />
}</td></tr>
<tr class="separator:a3caae3180358d7e623bcf2dc25e5b627"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_types_class_quant_lib_1_1_observer"><td colspan="2" onclick="javascript:toggleInherit('pub_types_class_quant_lib_1_1_observer')"><img src="closed.png" alt="-"/> Public Types inherited from <a class="el" href="class_quant_lib_1_1_observer.html">Observer</a></td></tr>
<tr class="memitem:a78de5f2b6bce96d718e3c18b9f52d67c inherit pub_types_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top"><a id="a78de5f2b6bce96d718e3c18b9f52d67c"></a>
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>
<tr class="separator:a78de5f2b6bce96d718e3c18b9f52d67c inherit pub_types_class_quant_lib_1_1_observer"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae98429250f6997df7b87f4b37454609e inherit pub_types_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top"><a id="ae98429250f6997df7b87f4b37454609e"></a>
typedef set_type::iterator </td><td class="memItemRight" valign="bottom"><b>iterator</b></td></tr>
<tr class="separator:ae98429250f6997df7b87f4b37454609e inherit pub_types_class_quant_lib_1_1_observer"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a9e13d7148b536a03183b655256e4ab41"><td class="memItemLeft" align="right" valign="top"><a id="a9e13d7148b536a03183b655256e4ab41"></a>
 </td><td class="memItemRight" valign="bottom"><b>AnalyticHestonEngine</b> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_heston_model.html">HestonModel</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>
<tr class="separator:a9e13d7148b536a03183b655256e4ab41"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:afc2a0a5d97c13025c0e27fba18e12c45"><td class="memItemLeft" align="right" valign="top"><a id="afc2a0a5d97c13025c0e27fba18e12c45"></a>
 </td><td class="memItemRight" valign="bottom"><b>AnalyticHestonEngine</b> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_heston_model.html">HestonModel</a> > &model, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> integrationOrder=144)</td></tr>
<tr class="separator:afc2a0a5d97c13025c0e27fba18e12c45"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af0191825a296d5a0f9a6ebf9f243f597"><td class="memItemLeft" align="right" valign="top"><a id="af0191825a296d5a0f9a6ebf9f243f597"></a>
 </td><td class="memItemRight" valign="bottom"><b>AnalyticHestonEngine</b> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_heston_model.html">HestonModel</a> > &model, ComplexLogFormula cpxLog, const Integration &itg, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> andersenPiterbargEpsilon=1e-8)</td></tr>
<tr class="separator:af0191825a296d5a0f9a6ebf9f243f597"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a02ddf3fecfe1bbd3c255725da023ab87"><td class="memItemLeft" align="right" valign="top"><a id="a02ddf3fecfe1bbd3c255725da023ab87"></a>
std::complex< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > </td><td class="memItemRight" valign="bottom"><b>chF</b> (const std::complex< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > &z, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t) const</td></tr>
<tr class="separator:a02ddf3fecfe1bbd3c255725da023ab87"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad5eab04a6188c028b8b1b3015e2814f3"><td class="memItemLeft" align="right" valign="top"><a id="ad5eab04a6188c028b8b1b3015e2814f3"></a>
std::complex< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > </td><td class="memItemRight" valign="bottom"><b>lnChF</b> (const std::complex< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > &z, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t) const</td></tr>
<tr class="separator:ad5eab04a6188c028b8b1b3015e2814f3"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a082ff96da379d5e17436372ccb3c0972"><td class="memItemLeft" align="right" valign="top"><a id="a082ff96da379d5e17436372ccb3c0972"></a>
void </td><td class="memItemRight" valign="bottom"><b>calculate</b> () const</td></tr>
<tr class="separator:a082ff96da379d5e17436372ccb3c0972"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a171352dc86e7106a631fa1e136f8a9e3"><td class="memItemLeft" align="right" valign="top"><a id="a171352dc86e7106a631fa1e136f8a9e3"></a>
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>numberOfEvaluations</b> () const</td></tr>
<tr class="separator:a171352dc86e7106a631fa1e136f8a9e3"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_class_quant_lib_1_1_generic_model_engine"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_generic_model_engine')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_generic_model_engine.html">GenericModelEngine< HestonModel, VanillaOption::arguments, VanillaOption::results ></a></td></tr>
<tr class="memitem:a3edb57d5adf68af0bd3ab7b6a1633edf inherit pub_methods_class_quant_lib_1_1_generic_model_engine"><td class="memItemLeft" align="right" valign="top"><a id="a3edb57d5adf68af0bd3ab7b6a1633edf"></a>
 </td><td class="memItemRight" valign="bottom"><b>GenericModelEngine</b> (const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_heston_model.html">HestonModel</a> > &model=<a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_heston_model.html">HestonModel</a> >())</td></tr>
<tr class="separator:a3edb57d5adf68af0bd3ab7b6a1633edf inherit pub_methods_class_quant_lib_1_1_generic_model_engine"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a5ccb95d65abe85dd75848c702a540e88 inherit pub_methods_class_quant_lib_1_1_generic_model_engine"><td class="memItemLeft" align="right" valign="top"><a id="a5ccb95d65abe85dd75848c702a540e88"></a>
 </td><td class="memItemRight" valign="bottom"><b>GenericModelEngine</b> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_heston_model.html">HestonModel</a> > &model)</td></tr>
<tr class="separator:a5ccb95d65abe85dd75848c702a540e88 inherit pub_methods_class_quant_lib_1_1_generic_model_engine"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_class_quant_lib_1_1_generic_engine"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_generic_engine')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_generic_engine.html">GenericEngine< VanillaOption::arguments, VanillaOption::results ></a></td></tr>
<tr class="memitem:a71b88a849e976521267094f05b679b4a inherit pub_methods_class_quant_lib_1_1_generic_engine"><td class="memItemLeft" align="right" valign="top"><a id="a71b88a849e976521267094f05b679b4a"></a>
PricingEngine::arguments * </td><td class="memItemRight" valign="bottom"><b>getArguments</b> () const</td></tr>
<tr class="separator:a71b88a849e976521267094f05b679b4a inherit pub_methods_class_quant_lib_1_1_generic_engine"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a444e176623e5142800ac5abd35556c10 inherit pub_methods_class_quant_lib_1_1_generic_engine"><td class="memItemLeft" align="right" valign="top"><a id="a444e176623e5142800ac5abd35556c10"></a>
const PricingEngine::results * </td><td class="memItemRight" valign="bottom"><b>getResults</b> () const</td></tr>
<tr class="separator:a444e176623e5142800ac5abd35556c10 inherit pub_methods_class_quant_lib_1_1_generic_engine"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad20897c5c8bd47f5d4005989bead0e55 inherit pub_methods_class_quant_lib_1_1_generic_engine"><td class="memItemLeft" align="right" valign="top"><a id="ad20897c5c8bd47f5d4005989bead0e55"></a>
void </td><td class="memItemRight" valign="bottom"><b>reset</b> ()</td></tr>
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<tr class="memitem:ac5c54df7ed3b930268c8d7752c101725 inherit pub_methods_class_quant_lib_1_1_generic_engine"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><b>update</b> ()</td></tr>
<tr class="separator:ac5c54df7ed3b930268c8d7752c101725 inherit pub_methods_class_quant_lib_1_1_generic_engine"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_class_quant_lib_1_1_pricing_engine"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_pricing_engine')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_pricing_engine.html">PricingEngine</a></td></tr>
<tr class="memitem:acadfc179f7be93951a88d8d9785402d3 inherit pub_methods_class_quant_lib_1_1_pricing_engine"><td class="memItemLeft" align="right" valign="top"><a id="acadfc179f7be93951a88d8d9785402d3"></a>
virtual arguments * </td><td class="memItemRight" valign="bottom"><b>getArguments</b> () const =0</td></tr>
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<tr class="memitem:ab7e33911413d94c4aa80aaf41eccddad inherit pub_methods_class_quant_lib_1_1_pricing_engine"><td class="memItemLeft" align="right" valign="top"><a id="ab7e33911413d94c4aa80aaf41eccddad"></a>
virtual const results * </td><td class="memItemRight" valign="bottom"><b>getResults</b> () const =0</td></tr>
<tr class="separator:ab7e33911413d94c4aa80aaf41eccddad inherit pub_methods_class_quant_lib_1_1_pricing_engine"><td class="memSeparator" colspan="2"> </td></tr>
<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>
<tr class="separator:a840dd96e33a304cbf681d357de7f48d0 inherit pub_methods_class_quant_lib_1_1_observable"><td class="memSeparator" colspan="2"> </td></tr>
<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>
<tr class="separator:a522aacdd0f2408fe5e46527a6db999b4 inherit pub_methods_class_quant_lib_1_1_observable"><td class="memSeparator" colspan="2"> </td></tr>
<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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<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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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-methods"></a>
Static Public Member Functions</h2></td></tr>
<tr class="memitem:a0e35cedf39ca505cd23a4e6516cdee3d"><td class="memItemLeft" align="right" valign="top"><a id="a0e35cedf39ca505cd23a4e6516cdee3d"></a>
static void </td><td class="memItemRight" valign="bottom"><b>doCalculation</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> riskFreeDiscount, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> dividendDiscount, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> spotPrice, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> strikePrice, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> term, <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> v0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> rho, const <a class="el" href="class_quant_lib_1_1_type_payoff.html">TypePayoff</a> &type, const Integration &integration, ComplexLogFormula cpxLog, const <a class="el" href="class_quant_lib_1_1_analytic_heston_engine.html">AnalyticHestonEngine</a> *enginePtr, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> &value, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> &evaluations)</td></tr>
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static ComplexLogFormula </td><td class="memItemRight" valign="bottom"><b>optimalControlVariate</b> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <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)</td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pro-methods"></a>
Protected Member Functions</h2></td></tr>
<tr class="memitem:af6a0ac6a6909199ea89886ed4cc59ada"><td class="memItemLeft" align="right" valign="top"><a id="af6a0ac6a6909199ea89886ed4cc59ada"></a>
virtual 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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</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_attribs_class_quant_lib_1_1_generic_model_engine"><td colspan="2" onclick="javascript:toggleInherit('pro_attribs_class_quant_lib_1_1_generic_model_engine')"><img src="closed.png" alt="-"/> Protected Attributes inherited from <a class="el" href="class_quant_lib_1_1_generic_model_engine.html">GenericModelEngine< HestonModel, VanillaOption::arguments, VanillaOption::results ></a></td></tr>
<tr class="memitem:a6864e2664edc95964c8d3c6325fbd30e inherit pro_attribs_class_quant_lib_1_1_generic_model_engine"><td class="memItemLeft" align="right" valign="top"><a id="a6864e2664edc95964c8d3c6325fbd30e"></a>
<a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_heston_model.html">HestonModel</a> > </td><td class="memItemRight" valign="bottom"><b>model_</b></td></tr>
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<tr class="inherit_header pro_attribs_class_quant_lib_1_1_generic_engine"><td colspan="2" onclick="javascript:toggleInherit('pro_attribs_class_quant_lib_1_1_generic_engine')"><img src="closed.png" alt="-"/> Protected Attributes inherited from <a class="el" href="class_quant_lib_1_1_generic_engine.html">GenericEngine< VanillaOption::arguments, VanillaOption::results ></a></td></tr>
<tr class="memitem:afee5e1b26214353757b120d9f5ad2169 inherit pro_attribs_class_quant_lib_1_1_generic_engine"><td class="memItemLeft" align="right" valign="top"><a id="afee5e1b26214353757b120d9f5ad2169"></a>
<a class="el" href="class_quant_lib_1_1_option_1_1arguments.html">VanillaOption::arguments</a> </td><td class="memItemRight" valign="bottom"><b>arguments_</b></td></tr>
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VanillaOption::results </td><td class="memItemRight" valign="bottom"><b>results_</b></td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>analytic Heston-model engine based on Fourier transform </p>
<p>Integration detail: Two algebraically equivalent formulations of the complex logarithm of the Heston model exist. Gatherals [2005] (also Duffie, Pan and <a class="el" href="class_quant_lib_1_1_singleton.html" title="Basic support for the singleton pattern.">Singleton</a> [2000], and Schoutens, Simons and Tistaert[2004]) version does not cause discoutinuities whereas the original version (e.g. Heston [1993]) needs some sort of "branch correction" to work properly. Gatheral's version does also work with adaptive integration routines and should be preferred over the original Heston version.</p>
<p>References:</p>
<p>Heston, Steven L., 1993. A Closed-Form Solution for Options with Stochastic Volatility with Applications to <a class="el" href="class_quant_lib_1_1_bond.html" title="Base bond class.">Bond</a> and <a class="el" href="class_quant_lib_1_1_currency.html" title="Currency specification">Currency</a> Options. The review of Financial Studies, Volume 6, Issue 2, 327-343.</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>
<p>R. Lord and C. Kahl, Why the rotation count algorithm works, <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=921335">http://papers.ssrn.com/sol3/papers.cfm?abstract_id=921335</a></p>
<p>H. Albrecher, P. Mayer, W.Schoutens and J. Tistaert, The Little Heston Trap, <a href="http://www.schoutens.be/HestonTrap.pdf">http://www.schoutens.be/HestonTrap.pdf</a></p>
<p>J. Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley Finance</p>
<p>F. Le Floc'h, Fourier Integration and Stochastic Volatility Calibration, <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2362968">https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2362968</a></p>
<p>L. Andersen, and V. Piterbarg, 2010, Interest Rate Modeling, Volume I: Foundations and Vanilla Models, Atlantic Financial Press London.</p>
<dl class="test"><dt><b><a class="el" href="test.html#_test000127">Tests:</a></b></dt><dd>the correctness of the returned value is tested by reproducing results available in web/literature and comparison with Black pricing. </dd></dl>
<dl class="section examples"><dt>Examples</dt><dd><a class="el" href="_equity_option_8cpp-example.html#_a29">EquityOption.cpp</a>.</dd>
</dl>
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