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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_black_karasinski.html">BlackKarasinski</a> </li>
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<a href="#pub-methods">Public Member Functions</a> </div>
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<div class="title">BlackKarasinski Class Reference<div class="ingroups"><a class="el" href="group__shortrate.html">Short-rate modelling framework</a></div></div> </div>
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<!-- doxytag: class="QuantLib::BlackKarasinski" --><!-- doxytag: inherits="QuantLib::OneFactorModel,QuantLib::TermStructureConsistentModel" -->
<p>Standard Black-Karasinski model class.
<a href="class_quant_lib_1_1_black_karasinski.html#details">More...</a></p>
<p><code>#include <ql/models/shortrate/onefactormodels/blackkarasinski.hpp></code></p>
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Inheritance diagram for BlackKarasinski:</div>
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<div class="center"><img src="class_quant_lib_1_1_black_karasinski__inherit__graph.png" border="0" usemap="#_black_karasinski_inherit__map" alt="Inheritance graph"/></div>
<map name="_black_karasinski_inherit__map" id="_black_karasinski_inherit__map">
<area shape="rect" id="node2" href="class_quant_lib_1_1_one_factor_model.html" title="Single-factor short-rate model abstract class." alt="" coords="5,6,123,37"/><area shape="rect" id="node4" href="class_quant_lib_1_1_term_structure_consistent_model.html" title="Term-structure consistent model class." alt="" coords="147,6,347,37"/></map>
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<p><a href="class_quant_lib_1_1_black_karasinski-members.html">List of all members.</a></p>
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Classes</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_black_karasinski_1_1_dynamics.html">Dynamics</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Short-rate dynamics in the Black-Karasinski model. <a href="class_quant_lib_1_1_black_karasinski_1_1_dynamics.html#details">More...</a><br/></td></tr>
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aadfac54b64d637fadf35d1c3cb7b7fc2"></a><!-- doxytag: member="QuantLib::BlackKarasinski::BlackKarasinski" ref="aadfac54b64d637fadf35d1c3cb7b7fc2" args="(const Handle< YieldTermStructure > &termStructure, Real a=0.1, Real sigma=0.1)" -->
 </td><td class="memItemRight" valign="bottom"><b>BlackKarasinski</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, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> a=0.1, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> sigma=0.1)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a89786edacdadb5904c317fd4ed5cb3bd"></a><!-- doxytag: member="QuantLib::BlackKarasinski::dynamics" ref="a89786edacdadb5904c317fd4ed5cb3bd" args="() const " -->
boost::shared_ptr<br class="typebreak"/>
< <a class="el" href="class_quant_lib_1_1_one_factor_model_1_1_short_rate_dynamics.html">ShortRateDynamics</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_black_karasinski.html#a89786edacdadb5904c317fd4ed5cb3bd">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" align="right" valign="top"><a class="anchor" id="a14130554fc69efb397b13bff53cc5eeb"></a><!-- doxytag: member="QuantLib::BlackKarasinski::tree" ref="a14130554fc69efb397b13bff53cc5eeb" args="(const TimeGrid &grid) const " -->
boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_lattice.html">Lattice</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_black_karasinski.html#a14130554fc69efb397b13bff53cc5eeb">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>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Standard Black-Karasinski model class. </p>
<p>This class implements the standard Black-Karasinski model defined by </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ d\ln r_t = (\theta(t) - \alpha \ln r_t)dt + \sigma dW_t, \]" src="form_292.png"/>
</p>
<p> where <img class="formulaInl" alt="$ alpha $" src="form_139.png"/> and <img class="formulaInl" alt="$ sigma $" src="form_140.png"/> are constants. </p>
<dl><dt><b>Examples: </b></dt><dd><a class="el" href="_bermudan_swaption_8cpp-example.html#_a33">BermudanSwaption.cpp</a>.</dd>
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