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<title>QuantLib: LocalVolCurve Class Reference</title>
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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<a class="el" href="class_quant_lib_1_1_local_vol_curve.html">LocalVolCurve</a></div>
<h1>LocalVolCurve Class Reference</h1><!-- doxytag: class="QuantLib::LocalVolCurve" --><!-- doxytag: inherits="QuantLib::LocalVolTermStructure" --><code>#include <ql/termstructures/volatility/equityfx/localvolcurve.hpp></code>
<p>
<div class="dynheader">
Inheritance diagram for LocalVolCurve:</div>
<div class="dynsection">
<p><center><img src="class_quant_lib_1_1_local_vol_curve__inherit__graph.png" border="0" usemap="#_local_vol_curve__inherit__map" alt="Inheritance graph"></center>
<map name="_local_vol_curve__inherit__map">
<area shape="rect" href="class_quant_lib_1_1_local_vol_term_structure.html" title="LocalVolTermStructure" alt="" coords="5,7,171,33"></map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
<p>
<a href="class_quant_lib_1_1_local_vol_curve-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Local volatility curve derived from a Black curve. <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="9bcfbba29fe0a01738bfb53056be256a"></a><!-- doxytag: member="QuantLib::LocalVolCurve::LocalVolCurve" ref="9bcfbba29fe0a01738bfb53056be256a" args="(const Handle< BlackVarianceCurve > &curve)" -->
</td><td class="memItemRight" valign="bottom"><b>LocalVolCurve</b> (const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_black_variance_curve.html">BlackVarianceCurve</a> > &curve)</td></tr>
<tr><td colspan="2"><div class="groupHeader">LocalVolTermStructure interface</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4a72314adf5959d9427df0fad16a1d3b"></a><!-- doxytag: member="QuantLib::LocalVolCurve::referenceDate" ref="4a72314adf5959d9427df0fad16a1d3b" args="() const " -->
const <a class="el" href="class_quant_lib_1_1_date.html">Date</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_local_vol_curve.html#4a72314adf5959d9427df0fad16a1d3b">referenceDate</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">the date at which discount = 1.0 and/or variance = 0.0 <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c147d63df367bbe5282b76b1f98cb9be"></a><!-- doxytag: member="QuantLib::LocalVolCurve::dayCounter" ref="c147d63df367bbe5282b76b1f98cb9be" args="() const " -->
<a class="el" href="class_quant_lib_1_1_day_counter.html">DayCounter</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_local_vol_curve.html#c147d63df367bbe5282b76b1f98cb9be">dayCounter</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">the day counter used for date/time conversion <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="74d8fc5480ca811db8332b7b30597fe9"></a><!-- doxytag: member="QuantLib::LocalVolCurve::maxDate" ref="74d8fc5480ca811db8332b7b30597fe9" args="() const " -->
<a class="el" href="class_quant_lib_1_1_date.html">Date</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_local_vol_curve.html#74d8fc5480ca811db8332b7b30597fe9">maxDate</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">the latest date for which the curve can return values <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ec700319eaa1c6fca66df8e15aea6167"></a><!-- doxytag: member="QuantLib::LocalVolCurve::minStrike" ref="ec700319eaa1c6fca66df8e15aea6167" 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_local_vol_curve.html#ec700319eaa1c6fca66df8e15aea6167">minStrike</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">the minimum strike for which the term structure can return vols <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="be69dc8630a5ea3f8333cfdfd01ba765"></a><!-- doxytag: member="QuantLib::LocalVolCurve::maxStrike" ref="be69dc8630a5ea3f8333cfdfd01ba765" 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_local_vol_curve.html#be69dc8630a5ea3f8333cfdfd01ba765">maxStrike</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">the maximum strike for which the term structure can return vols <br></td></tr>
<tr><td colspan="2"><div class="groupHeader">Visitability</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1d7eaf2f5dccce1c7781b54d64ba4a07"></a><!-- doxytag: member="QuantLib::LocalVolCurve::accept" ref="1d7eaf2f5dccce1c7781b54d64ba4a07" args="(AcyclicVisitor &)" -->
virtual void </td><td class="memItemRight" valign="bottom"><b>accept</b> (<a class="el" href="class_quant_lib_1_1_acyclic_visitor.html">AcyclicVisitor</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="el" href="group__types.html#gaa95ab7fe66935e3f7535413fad2a7d3">Volatility</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_local_vol_curve.html#ae14ca62291a64bc501d292224396525">localVolImpl</a> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a>, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>) const </td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="ae14ca62291a64bc501d292224396525"></a><!-- doxytag: member="QuantLib::LocalVolCurve::localVolImpl" ref="ae14ca62291a64bc501d292224396525" args="(Time, Real) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="group__types.html#gaa95ab7fe66935e3f7535413fad2a7d3">Volatility</a> localVolImpl </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t</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>dummy</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [protected, virtual]</code></td>
</tr>
</table>
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<p>
The relation <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \int_0^T \sigma_L^2(t)dt = \sigma_B^2 T \]" src="form_298.png">
<p>
holds, where <img class="formulaInl" alt="$ \sigma_L(t) $" src="form_299.png"> is the local volatility at time <img class="formulaInl" alt="$ t $" src="form_85.png"> and <img class="formulaInl" alt="$ \sigma_B(T) $" src="form_300.png"> is the Black volatility for maturity <img class="formulaInl" alt="$ T $" src="form_49.png">. From the above, the formula <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \sigma_L(t) = \sqrt{\frac{\mathrm{d}}{\mathrm{d}t}\sigma_B^2(t)t} \]" src="form_301.png">
<p>
can be deduced which is here implemented.
<p>Implements <a class="el" href="class_quant_lib_1_1_local_vol_term_structure.html#0b539b6f4f12c8e2835533e11e593c95">LocalVolTermStructure</a>.</p>
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