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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_hull_white.html">HullWhite</a></div>
<h1>HullWhite Class Reference<br>
<small>
[<a class="el" href="group__shortrate.html">Short-rate modelling framework</a>]</small>
</h1><!-- doxytag: class="QuantLib::HullWhite" --><!-- doxytag: inherits="QuantLib::Vasicek,QuantLib::TermStructureConsistentModel" --><code>#include <ql/ShortRateModels/OneFactorModels/hullwhite.hpp></code>
<p>
Inheritance diagram for HullWhite:<p><center><img src="class_quant_lib_1_1_hull_white__inherit__graph.png" border="0" usemap="#_hull_white__inherit__map" alt="Inheritance graph"></center>
<map name="_hull_white__inherit__map">
<area href="class_quant_lib_1_1_vasicek.html" shape="rect" coords="160,380,235,404" alt="">
<area href="class_quant_lib_1_1_one_factor_affine_model.html" shape="rect" coords="88,305,259,329" alt="">
<area href="class_quant_lib_1_1_one_factor_model.html" shape="rect" coords="5,231,136,255" alt="">
<area href="class_quant_lib_1_1_short_rate_model.html" shape="rect" coords="7,156,135,180" alt="">
<area href="class_quant_lib_1_1_calibrated_model.html" shape="rect" coords="19,81,149,105" alt="">
<area href="class_quant_lib_1_1_observer.html" shape="rect" coords="43,7,125,31" alt="">
<area href="class_quant_lib_1_1_observable.html" shape="rect" coords="161,7,260,31" alt="">
<area href="class_quant_lib_1_1_affine_model.html" shape="rect" coords="159,156,263,180" alt="">
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</map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center><a href="class_quant_lib_1_1_hull_white-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Single-factor Hull-White (extended Vasicek) model class.
<p>
This class implements the standard single-factor Hull-White model defined by <p class="formulaDsp">
<img class="formulaDsp" alt="\[ dr_t = (\theta(t) - \alpha r_t)dt + \sigma dW_t \]" src="form_214.png">
<p>
where <img class="formulaInl" alt="$ \alpha $" src="form_3.png"> and <img class="formulaInl" alt="$ \sigma $" src="form_4.png"> are constants.<p>
<dl compact><dt><b><a class="el" href="test.html#_test000114">Tests:</a></b></dt><dd>calibration results are tested against cached values</dd></dl>
<dl compact><dt><b><a class="el" href="bug.html#_bug000009">Bug:</a></b></dt><dd>When the term structure is relinked, the r0 parameter of the underlying <a class="el" href="class_quant_lib_1_1_vasicek.html">Vasicek</a> model is not updated.</dd></dl>
<dl compact><dt><b>Examples: </b></dt><dd>
<p>
<a class="el" href="_bermudan_swaption_8cpp-example.html#_a30">BermudanSwaption.cpp</a>.</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="5a576c1761c7ea4da9bb03a78b7ad5d5"></a><!-- doxytag: member="QuantLib::HullWhite::HullWhite" ref="5a576c1761c7ea4da9bb03a78b7ad5d5" args="(const Handle< YieldTermStructure > &termStructure, Real a=0.1, Real sigma=0.01)" -->
</td><td class="memItemRight" valign="bottom"><b>HullWhite</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> > &termStructure, Real a=0.1, Real sigma=0.01)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="140a7c576c87942d7f5a10db36affe8c"></a><!-- doxytag: member="QuantLib::HullWhite::tree" ref="140a7c576c87942d7f5a10db36affe8c" args="(const TimeGrid &grid) const " -->
boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_numerical_method.html">NumericalMethod</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white.html#140a7c576c87942d7f5a10db36affe8c">tree</a> (const <a class="el" href="class_quant_lib_1_1_time_grid.html">TimeGrid</a> &grid) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Return by default a trinomial recombining tree. <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="fc90527e32f5e84d191b5984cba8df45"></a><!-- doxytag: member="QuantLib::HullWhite::dynamics" ref="fc90527e32f5e84d191b5984cba8df45" args="() const" -->
boost::shared_ptr< ShortRateDynamics > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white.html#fc90527e32f5e84d191b5984cba8df45">dynamics</a> () const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the short-rate dynamics <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0b47448ed1ba48ac5138854aed3f1d49"></a><!-- doxytag: member="QuantLib::HullWhite::discountBondOption" ref="0b47448ed1ba48ac5138854aed3f1d49" args="(Option::Type type, Real strike, Time maturity, Time bondMaturity) const " -->
Real </td><td class="memItemRight" valign="bottom"><b>discountBondOption</b> (Option::Type type, Real strike, Time maturity, Time bondMaturity) const </td></tr>
<tr><td colspan="2"><br><h2>Static Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static <a class="el" href="group__types.html#gede435af51236692b1107d7639581d39">Rate</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white.html#f554e020436a6a21568f1149d61e2f54">convexityBias</a> (Real futurePrice, Time t, Time T, Real sigma, Real a)</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="4d8a7e8e132cf1dd8d1d9eac02f2bfae"></a><!-- doxytag: member="QuantLib::HullWhite::generateArguments" ref="4d8a7e8e132cf1dd8d1d9eac02f2bfae" args="()" -->
void </td><td class="memItemRight" valign="bottom"><b>generateArguments</b> ()</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cc348b40097f738841cc2b04eccb9ee3"></a><!-- doxytag: member="QuantLib::HullWhite::A" ref="cc348b40097f738841cc2b04eccb9ee3" args="(Time t, Time T) const" -->
Real </td><td class="memItemRight" valign="bottom"><b>A</b> (Time t, Time T) const</td></tr>
<tr><td colspan="2"><br><h2>Classes</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">class </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white_1_1_dynamics.html">Dynamics</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Short-rate dynamics in the Hull-White model. <a href="class_quant_lib_1_1_hull_white_1_1_dynamics.html#_details">More...</a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">class </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white_1_1_fitting_parameter.html">FittingParameter</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Analytical term-structure fitting parameter <img class="formulaInl" alt="$ \varphi(t) $" src="form_204.png">. <a href="class_quant_lib_1_1_hull_white_1_1_fitting_parameter.html#_details">More...</a><br></td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="f554e020436a6a21568f1149d61e2f54"></a><!-- doxytag: member="QuantLib::HullWhite::convexityBias" ref="f554e020436a6a21568f1149d61e2f54" args="(Real futurePrice, Time t, Time T, Real sigma, Real a)" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">static <a class="el" href="group__types.html#gede435af51236692b1107d7639581d39">Rate</a> convexityBias </td>
<td>(</td>
<td class="paramtype">Real </td>
<td class="paramname"> <em>futurePrice</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>t</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>T</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Real </td>
<td class="paramname"> <em>sigma</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Real </td>
<td class="paramname"> <em>a</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"><code> [static]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
Futures convexity bias (i.e., the difference between futures implied rate and forward rate) calculated as in G. Kirikos, D. Novak, "Convexity Conundrums", Risk Magazine, March 1997.<p>
<dl class="note" compact><dt><b>Note:</b></dt><dd>t and T should be expressed in yearfraction using deposit day counter, F_quoted is futures' market price. </dd></dl>
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