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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html">HullWhiteForwardProcess</a></div>
<h1>HullWhiteForwardProcess Class Reference<br>
<small>
[<a class="el" href="group__processes.html">Stochastic processes</a>]</small>
</h1><!-- doxytag: class="QuantLib::HullWhiteForwardProcess" --><!-- doxytag: inherits="QuantLib::ForwardMeasureProcess1D" --><code>#include <ql/processes/hullwhiteprocess.hpp></code>
<p>
<div class="dynheader">
Inheritance diagram for HullWhiteForwardProcess:</div>
<div class="dynsection">
<p><center><img src="class_quant_lib_1_1_hull_white_forward_process__inherit__graph.png" border="0" usemap="#_hull_white_forward_process__inherit__map" alt="Inheritance graph"></center>
<map name="_hull_white_forward_process__inherit__map">
<area shape="rect" href="class_quant_lib_1_1_forward_measure_process1_d.html" title="forward-measure 1-D stochastic process" alt="" coords="5,7,205,33"></map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
<p>
<a href="class_quant_lib_1_1_hull_white_forward_process-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Forward Hull-White stochastic process
<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="292686a7efcf2d88f2fa3f47a518adf5"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::HullWhiteForwardProcess" ref="292686a7efcf2d88f2fa3f47a518adf5" args="(const Handle< YieldTermStructure > &h, Real a, Real sigma)" -->
</td><td class="memItemRight" valign="bottom"><b>HullWhiteForwardProcess</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> > &h, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> a, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> sigma)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="eb6c2cfe0928889369fc49347418ce31"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::a" ref="eb6c2cfe0928889369fc49347418ce31" args="() const " -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>a</b> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="78bca11664a7d403bde6a9842f72ae61"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::sigma" ref="78bca11664a7d403bde6a9842f72ae61" args="() const " -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>sigma</b> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="65387ea280e5a966d21a2a97988acee2"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::alpha" ref="65387ea280e5a966d21a2a97988acee2" args="(Time t) const " -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>alpha</b> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bbd0955abb6212e7d7b3a740f4e9df5e"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::M_T" ref="bbd0955abb6212e7d7b3a740f4e9df5e" args="(Real s, Real t, Real T) const " -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>M_T</b> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> s, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> t, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> T) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="18613e934dfda1a1db8f8f4d8b00eaae"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::B" ref="18613e934dfda1a1db8f8f4d8b00eaae" args="(Time t, Time T) const " -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>B</b> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> T) const </td></tr>
<tr><td colspan="2"><div class="groupHeader">StochasticProcess1D interface</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="89d2f497b5fd0d0a0dce2ec82c86e778"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::x0" ref="89d2f497b5fd0d0a0dce2ec82c86e778" args="() const " -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#89d2f497b5fd0d0a0dce2ec82c86e778">x0</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the initial value of the state variable <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="545d33724b1d6d312eb8a17f73571842"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::drift" ref="545d33724b1d6d312eb8a17f73571842" args="(Time t, Real x) const " -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#545d33724b1d6d312eb8a17f73571842">drift</a> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</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, x_t) $" src="form_279.png"> <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b4d7fe4af7a6dd0ae710c073569821e4"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::diffusion" ref="b4d7fe4af7a6dd0ae710c073569821e4" args="(Time t, Real x) const " -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#b4d7fe4af7a6dd0ae710c073569821e4">diffusion</a> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the diffusion part of the equation, i.e. <img class="formulaInl" alt="$ \sigma(t, x_t) $" src="form_280.png"> <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#81842299056bb82662dce099fca6bcba">expectation</a> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x0, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#a78ac261543c5f8c3b2e065f4a57c526">stdDeviation</a> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x0, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#ec618e405b3e8c104f58b6616d3d482f">variance</a> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x0, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a096533d7873ed281f49dd62f15f5bea"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::process_" ref="a096533d7873ed281f49dd62f15f5bea" args="" -->
boost::shared_ptr<br>
< <a class="el" href="class_quant_lib_1_1_ornstein_uhlenbeck_process.html">QuantLib::OrnsteinUhlenbeckProcess</a> > </td><td class="memItemRight" valign="bottom"><b>process_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1bd1a2c715721bf9b2d0649bc8be4a98"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::h_" ref="1bd1a2c715721bf9b2d0649bc8be4a98" args="" -->
<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>h_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="114bd3f70557109ba551776610bb2dc1"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::a_" ref="114bd3f70557109ba551776610bb2dc1" args="" -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>a_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="37293181f9beea97f75b133deb9d9119"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::sigma_" ref="37293181f9beea97f75b133deb9d9119" args="" -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>sigma_</b></td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="81842299056bb82662dce099fca6bcba"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::expectation" ref="81842299056bb82662dce099fca6bcba" args="(Time t0, Real x0, Time dt) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> expectation </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>x0</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>dt</em></td><td> </td>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
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<p>
returns the expectation <img class="formulaInl" alt="$ E(x_{t_0 + \Delta t} | x_{t_0} = x_0) $" src="form_281.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_273.png"> according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#8be83040b1b61f27a482f14d5b461caa">StochasticProcess1D</a>.</p>
</div>
</div><p>
<a class="anchor" name="a78ac261543c5f8c3b2e065f4a57c526"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::stdDeviation" ref="a78ac261543c5f8c3b2e065f4a57c526" args="(Time t0, Real x0, Time dt) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> stdDeviation </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t0</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>x0</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>dt</em></td><td> </td>
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<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
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<p>
returns the standard deviation <img class="formulaInl" alt="$ S(x_{t_0 + \Delta t} | x_{t_0} = x_0) $" src="form_282.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_273.png"> according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#36c51f5c5f2c6dd353751857c3625ca7">StochasticProcess1D</a>.</p>
</div>
</div><p>
<a class="anchor" name="ec618e405b3e8c104f58b6616d3d482f"></a><!-- doxytag: member="QuantLib::HullWhiteForwardProcess::variance" ref="ec618e405b3e8c104f58b6616d3d482f" args="(Time t0, Real x0, Time dt) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> variance </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t0</em>, </td>
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<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>x0</em>, </td>
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<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>dt</em></td><td> </td>
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<p>
returns the variance <img class="formulaInl" alt="$ V(x_{t_0 + \Delta t} | x_{t_0} = x_0) $" src="form_283.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_273.png"> according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#b0dfe97f905be74f88809dec0c56b998">StochasticProcess1D</a>.</p>
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