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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_abcd.html">Abcd</a></div>
<h1>Abcd Class Reference</h1><!-- doxytag: class="QuantLib::Abcd" --><!-- doxytag: inherits="std::unary_function" --><code>#include <ql/MarketModels/Models/abcd.hpp></code>
<p>
<a href="class_quant_lib_1_1_abcd-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
<a class="el" href="class_quant_lib_1_1_abcd.html">Abcd</a> functional form for instantaneous volatility.
<p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ f(T-t) = [ a + b(T-t) ] e^{-c(T-t)} + d \]" src="form_77.png">
<p>
<p>
following Rebonato notation.
<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="2010f5f60032dc63c98c8572b29c53c2"></a><!-- doxytag: member="QuantLib::Abcd::Abcd" ref="2010f5f60032dc63c98c8572b29c53c2" args="(Real a=-0.06, Real b=0.17, Real c=0.54, Real d=0.17, bool aIsFixed=false, bool bIsFixed=false, bool cIsFixed=false, bool dIsFixed=false)" -->
</td><td class="memItemRight" valign="bottom"><b>Abcd</b> (Real a=-0.06, Real b=0.17, Real c=0.54, Real d=0.17, bool aIsFixed=false, bool bIsFixed=false, bool cIsFixed=false, bool dIsFixed=false)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="24c13811a6f048568243bc3246230ded"></a><!-- doxytag: member="QuantLib::Abcd::operator()" ref="24c13811a6f048568243bc3246230ded" args="(Time u) const" -->
Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#24c13811a6f048568243bc3246230ded">operator()</a> (Time u) const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">instantaneous volatility at time to maturity u: <p class="formulaDsp">
<img class="formulaDsp" alt="\[ f(u) \]" src="form_78.png">
<p>
<br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="962375e1380660f0a2fe72e737e3950b"></a><!-- doxytag: member="QuantLib::Abcd::a" ref="962375e1380660f0a2fe72e737e3950b" args="() const" -->
Real </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="3bb198a929fb62eabaf6b36385eb2416"></a><!-- doxytag: member="QuantLib::Abcd::b" ref="3bb198a929fb62eabaf6b36385eb2416" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>b</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="88c56f33e77874ce043c8b42605c585b"></a><!-- doxytag: member="QuantLib::Abcd::c" ref="88c56f33e77874ce043c8b42605c585b" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>c</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="350fbde97c9e00ce0c4e479e3f5401c4"></a><!-- doxytag: member="QuantLib::Abcd::d" ref="350fbde97c9e00ce0c4e479e3f5401c4" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>d</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#0516e6e38c5724ea294e80bec137f019">instantaneousVolatility</a> (Time u, Time T) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#08c27703b2295ac56b385e836688e845">instantaneousVariance</a> (Time u, Time T) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#8328c6d656f7f073152ee07bfa2710d6">instantaneousCovariance</a> (Time u, Time T, Time S) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#8cb61b56678e3b0ff29ab34cec645c0a">volatility</a> (Time tMin, Time tMax, Time T) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#f9d4a81d4eb448d018b288ed6f07ad78">variance</a> (Time tMin, Time tMax, Time T) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#05ce5a1300733331c74036c2be035392">covariance</a> (Time tMin, Time tMax, Time T, Time S) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0835e3739c52b2cc23886509f3fd583a"></a><!-- doxytag: member="QuantLib::Abcd::shortTermVolatility" ref="0835e3739c52b2cc23886509f3fd583a" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#0835e3739c52b2cc23886509f3fd583a">shortTermVolatility</a> () const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">instantaneous volatility when time to maturity = 0.0 <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="12504f51b92de1f056807e8e1e8f08f6"></a><!-- doxytag: member="QuantLib::Abcd::longTermVolatility" ref="12504f51b92de1f056807e8e1e8f08f6" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#12504f51b92de1f056807e8e1e8f08f6">longTermVolatility</a> () const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">instantaneous volatility when time to maturity = +inf <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c0cc0e5c0826bd5cec9aaa29288e845a"></a><!-- doxytag: member="QuantLib::Abcd::maximumLocation" ref="c0cc0e5c0826bd5cec9aaa29288e845a" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#c0cc0e5c0826bd5cec9aaa29288e845a">maximumLocation</a> () const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">time to maturity at which the instantaneous volatility reaches maximum (if any) <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="43d85604f6420e95bae925cdca003141"></a><!-- doxytag: member="QuantLib::Abcd::maximumVolatility" ref="43d85604f6420e95bae925cdca003141" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#43d85604f6420e95bae925cdca003141">maximumVolatility</a> () const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">maximum of the instantaneous volatility <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6022cffd54aac1bd5e8777b7d5ff9929"></a><!-- doxytag: member="QuantLib::Abcd::k" ref="6022cffd54aac1bd5e8777b7d5ff9929" args="(const std::vector< Real > &blackVols, const std::vector< Real >::const_iterator &t) const" -->
std::vector< Real > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#6022cffd54aac1bd5e8777b7d5ff9929">k</a> (const std::vector< Real > &blackVols, const std::vector< Real >::const_iterator &t) const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">adjustment factors needed to match Black vols <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2bfe4e461c7bc53d6f173fad3aa87a4c"></a><!-- doxytag: member="QuantLib::Abcd::error" ref="2bfe4e461c7bc53d6f173fad3aa87a4c" args="(const std::vector< Real > &blackVols, const std::vector< Real >::const_iterator &t) const" -->
Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#2bfe4e461c7bc53d6f173fad3aa87a4c">error</a> (const std::vector< Real > &blackVols, const std::vector< Real >::const_iterator &t) const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">vol error <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="79f435ffe58ec505560e3663ffa9373c"></a><!-- doxytag: member="QuantLib::Abcd::capletCalibration" ref="79f435ffe58ec505560e3663ffa9373c" args="(const std::vector< Real > &blackVols, const std::vector< Real >::const_iterator &t, const boost::shared_ptr< OptimizationMethod > &method=boost::shared_ptr< OptimizationMethod >())" -->
EndCriteria::Type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_abcd.html#79f435ffe58ec505560e3663ffa9373c">capletCalibration</a> (const std::vector< Real > &blackVols, const std::vector< Real >::const_iterator &t, const boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_optimization_method.html">OptimizationMethod</a> > &method=boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_optimization_method.html">OptimizationMethod</a> >())</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">calibration <br></td></tr>
<tr><td colspan="2"><br><h2>Friends</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="276745f940145c5d975b9471fdd9b6dd"></a><!-- doxytag: member="QuantLib::Abcd::AbcdCostFunction" ref="276745f940145c5d975b9471fdd9b6dd" args="" -->
class </td><td class="memItemRight" valign="bottom"><b>AbcdCostFunction</b></td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="0516e6e38c5724ea294e80bec137f019"></a><!-- doxytag: member="QuantLib::Abcd::instantaneousVolatility" ref="0516e6e38c5724ea294e80bec137f019" args="(Time u, Time T) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">Real instantaneousVolatility </td>
<td>(</td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>u</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>T</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const</td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
instantaneous volatility at time u of the T-fixing rate: <p class="formulaDsp">
<img class="formulaDsp" alt="\[ f(T-u) \]" src="form_79.png">
<p>
</div>
</div><p>
<a class="anchor" name="08c27703b2295ac56b385e836688e845"></a><!-- doxytag: member="QuantLib::Abcd::instantaneousVariance" ref="08c27703b2295ac56b385e836688e845" args="(Time u, Time T) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">Real instantaneousVariance </td>
<td>(</td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>u</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>T</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const</td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
instantaneous variance at time u of T-fixing rate: <p class="formulaDsp">
<img class="formulaDsp" alt="\[ f(T-u)f(T-u) \]" src="form_80.png">
<p>
</div>
</div><p>
<a class="anchor" name="8328c6d656f7f073152ee07bfa2710d6"></a><!-- doxytag: member="QuantLib::Abcd::instantaneousCovariance" ref="8328c6d656f7f073152ee07bfa2710d6" args="(Time u, Time T, Time S) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">Real instantaneousCovariance </td>
<td>(</td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>u</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>S</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const</td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
instantaneous covariance at time u between T and S fixing rates: <p class="formulaDsp">
<img class="formulaDsp" alt="\[ f(T-u)f(S-u) \]" src="form_81.png">
<p>
</div>
</div><p>
<a class="anchor" name="8cb61b56678e3b0ff29ab34cec645c0a"></a><!-- doxytag: member="QuantLib::Abcd::volatility" ref="8cb61b56678e3b0ff29ab34cec645c0a" args="(Time tMin, Time tMax, Time T) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">Real volatility </td>
<td>(</td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>tMin</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>tMax</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>T</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const</td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
volatility in [tMin,tMax] of T-fixing rate: <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \sqrt{ \int_{tMin}^{tMax} f^2(T-u)du }\]" src="form_82.png">
<p>
</div>
</div><p>
<a class="anchor" name="f9d4a81d4eb448d018b288ed6f07ad78"></a><!-- doxytag: member="QuantLib::Abcd::variance" ref="f9d4a81d4eb448d018b288ed6f07ad78" args="(Time tMin, Time tMax, Time T) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">Real variance </td>
<td>(</td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>tMin</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>tMax</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>T</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const</td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
variance in [tMin,tMax] of T-fixing rate: <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \int_{tMin}^{tMax} f^2(T-u)du \]" src="form_83.png">
<p>
</div>
</div><p>
<a class="anchor" name="05ce5a1300733331c74036c2be035392"></a><!-- doxytag: member="QuantLib::Abcd::covariance" ref="05ce5a1300733331c74036c2be035392" args="(Time tMin, Time tMax, Time T, Time S) const" -->
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<td class="memname">Real covariance </td>
<td>(</td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>tMin</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>tMax</em>, </td>
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<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>T</em>, </td>
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<td class="paramtype">Time </td>
<td class="paramname"> <em>S</em></td><td> </td>
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<td>)</td>
<td></td><td></td><td width="100%"> const</td>
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<p>
covariance in [tMin,tMax] between T and S fixing rates: <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \int_{tMin}^{tMax} f(T-u)f(S-u)du \]" src="form_84.png">
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