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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_generalized_black_scholes_process.html">GeneralizedBlackScholesProcess</a></li> </ul>
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<div class="title">GeneralizedBlackScholesProcess Class Reference<div class="ingroups"><a class="el" href="group__processes.html">Stochastic processes</a></div></div> </div>
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<p>Generalized Black-Scholes stochastic process.
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<p><code>#include <ql/processes/blackscholesprocess.hpp></code></p>
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<table class="memberdecls">
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Public Member Functions</h2></td></tr>
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 </td><td class="memItemRight" valign="bottom"><b>GeneralizedBlackScholesProcess</b> (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> > &<a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ae7a72a4c8dd1f131143d89a535765d42">x0</a>, 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> > &dividendTS, 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> > &riskFreeTS, const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_black_vol_term_structure.html">BlackVolTermStructure</a> > &blackVolTS, const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">discretization</a> > &d=ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">discretization</a> >(new <a class="el" href="class_quant_lib_1_1_euler_discretization.html">EulerDiscretization</a>), bool forceDiscretization=false)</td></tr>
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 </td><td class="memItemRight" valign="bottom"><b>GeneralizedBlackScholesProcess</b> (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> > &<a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ae7a72a4c8dd1f131143d89a535765d42">x0</a>, 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> > &dividendTS, 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> > &riskFreeTS, const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_black_vol_term_structure.html">BlackVolTermStructure</a> > &blackVolTS, const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_local_vol_term_structure.html">LocalVolTermStructure</a> > &localVolTS)</td></tr>
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<tr><td colspan="2"><div class="groupHeader">StochasticProcess1D interface</div></td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ae7a72a4c8dd1f131143d89a535765d42">x0</a> () const</td></tr>
<tr class="memdesc:ae7a72a4c8dd1f131143d89a535765d42"><td class="mdescLeft"> </td><td class="mdescRight">returns the initial value of the state variable <br /></td></tr>
<tr class="separator:ae7a72a4c8dd1f131143d89a535765d42"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac0fef0634785539f761f09c6fe6fa566"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ac0fef0634785539f761f09c6fe6fa566">drift</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const</td></tr>
<tr class="separator:ac0fef0634785539f761f09c6fe6fa566"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a5ab4b67d548a4674f8a989868c0a922b"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#a5ab4b67d548a4674f8a989868c0a922b">diffusion</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const</td></tr>
<tr class="separator:a5ab4b67d548a4674f8a989868c0a922b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a181565755d35d36c7bf732e1905f3661"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#a181565755d35d36c7bf732e1905f3661">apply</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ae7a72a4c8dd1f131143d89a535765d42">x0</a>, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> dx) const</td></tr>
<tr class="separator:a181565755d35d36c7bf732e1905f3661"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af718d7a907863b462830ca96dda4321c"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#af718d7a907863b462830ca96dda4321c">expectation</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ae7a72a4c8dd1f131143d89a535765d42">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const</td></tr>
<tr class="separator:af718d7a907863b462830ca96dda4321c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac731332c432f5be07edc3bda917e6ea0"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ac731332c432f5be07edc3bda917e6ea0">stdDeviation</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ae7a72a4c8dd1f131143d89a535765d42">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const</td></tr>
<tr class="separator:ac731332c432f5be07edc3bda917e6ea0"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a5da3e29d59b0c10b20f760739de77535"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#a5da3e29d59b0c10b20f760739de77535">variance</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ae7a72a4c8dd1f131143d89a535765d42">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const</td></tr>
<tr class="separator:a5da3e29d59b0c10b20f760739de77535"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa81fd19ade75674de0a4bcbacd4a26ba"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#aa81fd19ade75674de0a4bcbacd4a26ba">evolve</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ae7a72a4c8dd1f131143d89a535765d42">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> dw) 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_generalized_black_scholes_process.html#ab2e3e42e764f5a50686da1cb9ea153be">time</a> (const <a class="el" href="class_quant_lib_1_1_date.html">Date</a> &) const</td></tr>
<tr class="separator:ab2e3e42e764f5a50686da1cb9ea153be"><td class="memSeparator" colspan="2"> </td></tr>
<tr><td colspan="2"><div class="groupHeader">Observer interface</div></td></tr>
<tr class="memitem:ac5c54df7ed3b930268c8d7752c101725"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#ac5c54df7ed3b930268c8d7752c101725">update</a> ()</td></tr>
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<tr class="inherit_header pub_methods_class_quant_lib_1_1_stochastic_process1_d"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_stochastic_process1_d')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a></td></tr>
<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:a33d9dda89ba7db93ae8b7d8c64122597 inherit pub_methods_class_quant_lib_1_1_stochastic_process"><td class="memItemLeft" align="right" valign="top"><a id="a33d9dda89ba7db93ae8b7d8c64122597"></a>
virtual <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_stochastic_process.html#a33d9dda89ba7db93ae8b7d8c64122597">factors</a> () const</td></tr>
<tr class="memdesc:a33d9dda89ba7db93ae8b7d8c64122597 inherit pub_methods_class_quant_lib_1_1_stochastic_process"><td class="mdescLeft"> </td><td class="mdescRight">returns the number of independent factors of the process <br /></td></tr>
<tr class="separator:a33d9dda89ba7db93ae8b7d8c64122597 inherit pub_methods_class_quant_lib_1_1_stochastic_process"><td class="memSeparator" colspan="2"> </td></tr>
<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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<tr class="memitem:aa6ade205ed506bf712da2704f80a73a0 inherit pub_methods_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top"><a id="aa6ade205ed506bf712da2704f80a73a0"></a>
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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<tr class="memitem:a4ce7359ad0f73a54dba555be24855804 inherit pub_methods_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top"><a id="a4ce7359ad0f73a54dba555be24855804"></a>
<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>
<tr class="separator:a3d53f9669c128dadc74a5d044a7c8e68 inherit pub_methods_class_quant_lib_1_1_observer"><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>
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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>
<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>
<tr class="separator:a397546715bfc5aedd1d16dd202a19d4c inherit pub_methods_class_quant_lib_1_1_observable"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="member-group"></a>
Inspectors</h2></td></tr>
<tr class="memitem:a240681a98889c2f0c37a1a1e6a3b6455"><td class="memItemLeft" align="right" valign="top"><a id="a240681a98889c2f0c37a1a1e6a3b6455"></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>stateVariable</b> () const</td></tr>
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<tr class="memitem:a8b96bfefd25ed4845f6fe24a80e91665"><td class="memItemLeft" align="right" valign="top"><a id="a8b96bfefd25ed4845f6fe24a80e91665"></a>
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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<tr class="memitem:aecedd71bbe2a44bed902daa89136165c"><td class="memItemLeft" align="right" valign="top"><a id="aecedd71bbe2a44bed902daa89136165c"></a>
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:a61aa22268c07f1b253947b077619dbfd"><td class="memItemLeft" align="right" valign="top"><a id="a61aa22268c07f1b253947b077619dbfd"></a>
const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_black_vol_term_structure.html">BlackVolTermStructure</a> > & </td><td class="memItemRight" valign="bottom"><b>blackVolatility</b> () const</td></tr>
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<tr class="memitem:a0457d39220524e7c7b3512d5a9c4e07d"><td class="memItemLeft" align="right" valign="top"><a id="a0457d39220524e7c7b3512d5a9c4e07d"></a>
const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_local_vol_term_structure.html">LocalVolTermStructure</a> > & </td><td class="memItemRight" valign="bottom"><b>localVolatility</b> () 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 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>
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<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>
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<tr class="inherit_header pro_methods_class_quant_lib_1_1_stochastic_process1_d"><td colspan="2" onclick="javascript:toggleInherit('pro_methods_class_quant_lib_1_1_stochastic_process1_d')"><img src="closed.png" alt="-"/> Protected Member Functions inherited from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a></td></tr>
<tr class="memitem:ad98007dd5c830d050dfb0d4205094b9e inherit pro_methods_class_quant_lib_1_1_stochastic_process1_d"><td class="memItemLeft" align="right" valign="top"><a id="ad98007dd5c830d050dfb0d4205094b9e"></a>
 </td><td class="memItemRight" valign="bottom"><b>StochasticProcess1D</b> ()</td></tr>
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<tr class="memitem:a7119a443854b505713e5e409dc6bf3e7 inherit pro_methods_class_quant_lib_1_1_stochastic_process1_d"><td class="memItemLeft" align="right" valign="top"><a id="a7119a443854b505713e5e409dc6bf3e7"></a>
 </td><td class="memItemRight" valign="bottom"><b>StochasticProcess1D</b> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html">discretization</a> > &)</td></tr>
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<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="inherit_header pro_attribs_class_quant_lib_1_1_stochastic_process1_d"><td colspan="2" onclick="javascript:toggleInherit('pro_attribs_class_quant_lib_1_1_stochastic_process1_d')"><img src="closed.png" alt="-"/> Protected Attributes inherited from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a></td></tr>
<tr class="memitem:a51a940500df8f947d270aaab06f53371 inherit pro_attribs_class_quant_lib_1_1_stochastic_process1_d"><td class="memItemLeft" align="right" valign="top"><a id="a51a940500df8f947d270aaab06f53371"></a>
ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html">discretization</a> > </td><td class="memItemRight" valign="bottom"><b>discretization_</b></td></tr>
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<tr class="inherit_header pro_attribs_class_quant_lib_1_1_stochastic_process"><td colspan="2" onclick="javascript:toggleInherit('pro_attribs_class_quant_lib_1_1_stochastic_process')"><img src="closed.png" alt="-"/> Protected Attributes inherited from <a class="el" href="class_quant_lib_1_1_stochastic_process.html">StochasticProcess</a></td></tr>
<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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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Generalized Black-Scholes stochastic process. </p>
<p>This class describes the stochastic process \( S \) governed by </p><p class="formulaDsp">
\[ d\ln S(t) = (r(t) - q(t) - \frac{\sigma(t, S)^2}{2}) dt + \sigma dW_t. \]
</p>
<dl class="caveats"><dt><b><a class="el" href="caveats.html#_caveats000148">Warning:</a></b></dt><dd>while the interface is expressed in terms of \( S \), the internal calculations work on \( ln S \).</dd></dl>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a id="ac0fef0634785539f761f09c6fe6fa566"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac0fef0634785539f761f09c6fe6fa566">◆ </a></span>drift()</h2>
<div class="memitem">
<div class="memproto">
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<td class="mlabels-left">
<table class="memname">
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<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> drift </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>t</em>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>x</em> </td>
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<td>)</td>
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<p>Implements <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#a6bded8896a46fad4d189950552432cd3">StochasticProcess1D</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a5ab4b67d548a4674f8a989868c0a922b">◆ </a></span>diffusion()</h2>
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<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> diffusion </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>t</em>, </td>
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<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>x</em> </td>
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<p>Implements <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#afaf479da3baa52185b369071b1689d89">StochasticProcess1D</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a181565755d35d36c7bf732e1905f3661">◆ </a></span>apply()</h2>
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<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> apply </td>
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<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
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<p>applies a change to the asset value. By default, it returns \( x + \Delta x \). </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#a6c8e95cb5b48a9ca86fef990c92c58c9">StochasticProcess1D</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#af718d7a907863b462830ca96dda4321c">◆ </a></span>expectation()</h2>
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<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> expectation </td>
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<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>x0</em>, </td>
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<dl class="caveats"><dt><b><a class="el" href="caveats.html#_caveats000152">Warning:</a></b></dt><dd>in general raises a "not implemented" exception. It should be rewritten to return the expectation E(S) of the process, not exp(E(log S)). </dd></dl>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#aee564ee8adf46c50265cd990b1dcd8a3">StochasticProcess1D</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ac731332c432f5be07edc3bda917e6ea0">◆ </a></span>stdDeviation()</h2>
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<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> stdDeviation </td>
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<p>returns the standard deviation \( S(x_{t_0 + \Delta t} | x_{t_0} = x_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization. </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#abb8a7016bec7d28872df221fb8995853">StochasticProcess1D</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a5da3e29d59b0c10b20f760739de77535">◆ </a></span>variance()</h2>
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<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> variance </td>
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<p>returns the variance \( V(x_{t_0 + \Delta t} | x_{t_0} = x_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization. </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#a5e92435fcc5c43be09e627494cf7a9d0">StochasticProcess1D</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aa81fd19ade75674de0a4bcbacd4a26ba">◆ </a></span>evolve()</h2>
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<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> evolve </td>
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<td class="paramname"><em>dw</em> </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">
\[ E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w \]
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<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_process1_d.html#a096b196eb0c6e453acbd428ae378c7de">StochasticProcess1D</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>
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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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<h2 class="memtitle"><span class="permalink"><a href="#ac5c54df7ed3b930268c8d7752c101725">◆ </a></span>update()</h2>
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<td class="memname">void update </td>
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<p>This method must be implemented in derived classes. An instance of Observer does not call this method directly: instead, it will be called by the observables the instance registered with when they need to notify any changes. </p>
<p>Implements <a class="el" href="class_quant_lib_1_1_observer.html#a99b02345a8a15d3c5ea2844a2253f510">Observer</a>.</p>
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