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<li class="navelem"><b>QuantLib</b> </li>
<li class="navelem"><a class="el" href="class_quant_lib_1_1_local_vol_curve.html">LocalVolCurve</a> </li>
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<a href="#pub-methods">Public Member Functions</a> |
<a href="#pro-methods">Protected Member Functions</a> </div>
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<div class="title">LocalVolCurve Class Reference</div> </div>
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<!-- doxytag: class="QuantLib::LocalVolCurve" --><!-- doxytag: inherits="QuantLib::LocalVolTermStructure" -->
<p>Local volatility curve derived from a Black curve.
<a href="class_quant_lib_1_1_local_vol_curve.html#details">More...</a></p>
<p><code>#include <ql/termstructures/volatility/equityfx/localvolcurve.hpp></code></p>
<div class="dynheader">
Inheritance diagram for LocalVolCurve:</div>
<div class="dyncontent">
<div class="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"/></div>
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<area shape="rect" id="node2" href="class_quant_lib_1_1_local_vol_term_structure.html" title="LocalVolTermStructure" alt="" coords="5,6,157,37"/></map>
<center><span class="legend">[<a href="graph_legend.html">legend</a>]</span></center></div>
<p><a href="class_quant_lib_1_1_local_vol_curve-members.html">List of all members.</a></p>
<table class="memberdecls">
<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="a9bcfbba29fe0a01738bfb53056be256a"></a><!-- doxytag: member="QuantLib::LocalVolCurve::LocalVolCurve" ref="a9bcfbba29fe0a01738bfb53056be256a" 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">TermStructure interface</div></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a4a72314adf5959d9427df0fad16a1d3b"></a><!-- doxytag: member="QuantLib::LocalVolCurve::referenceDate" ref="a4a72314adf5959d9427df0fad16a1d3b" 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#a4a72314adf5959d9427df0fad16a1d3b">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" align="right" valign="top"><a class="anchor" id="ae9a0f3904cff2fe61596c593dd0b6448"></a><!-- doxytag: member="QuantLib::LocalVolCurve::calendar" ref="ae9a0f3904cff2fe61596c593dd0b6448" args="() const " -->
<a class="el" href="class_quant_lib_1_1_calendar.html">Calendar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_local_vol_curve.html#ae9a0f3904cff2fe61596c593dd0b6448">calendar</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">the calendar used for reference and/or option date calculation <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ac147d63df367bbe5282b76b1f98cb9be"></a><!-- doxytag: member="QuantLib::LocalVolCurve::dayCounter" ref="ac147d63df367bbe5282b76b1f98cb9be" 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#ac147d63df367bbe5282b76b1f98cb9be">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" align="right" valign="top"><a class="anchor" id="a74d8fc5480ca811db8332b7b30597fe9"></a><!-- doxytag: member="QuantLib::LocalVolCurve::maxDate" ref="a74d8fc5480ca811db8332b7b30597fe9" 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#a74d8fc5480ca811db8332b7b30597fe9">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 colspan="2"><div class="groupHeader">VolatilityTermStructure interface</div></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aec700319eaa1c6fca66df8e15aea6167"></a><!-- doxytag: member="QuantLib::LocalVolCurve::minStrike" ref="aec700319eaa1c6fca66df8e15aea6167" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_local_vol_curve.html#aec700319eaa1c6fca66df8e15aea6167">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" align="right" valign="top"><a class="anchor" id="abe69dc8630a5ea3f8333cfdfd01ba765"></a><!-- doxytag: member="QuantLib::LocalVolCurve::maxStrike" ref="abe69dc8630a5ea3f8333cfdfd01ba765" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_local_vol_curve.html#abe69dc8630a5ea3f8333cfdfd01ba765">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" align="right" valign="top"><a class="anchor" id="a1d7eaf2f5dccce1c7781b54d64ba4a07"></a><!-- doxytag: member="QuantLib::LocalVolCurve::accept" ref="a1d7eaf2f5dccce1c7781b54d64ba4a07" 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"><h2><a name="pro-methods"></a>
Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#gaaa95ab7fe66935e3f7535413fad2a7d3">Volatility</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_local_vol_curve.html#aae14ca62291a64bc501d292224396525">localVolImpl</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a>, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>) const </td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Local volatility curve derived from a Black curve. </p>
</div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="aae14ca62291a64bc501d292224396525"></a><!-- doxytag: member="QuantLib::LocalVolCurve::localVolImpl" ref="aae14ca62291a64bc501d292224396525" args="(Time, Real) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname"><a class="el" href="group__types.html#gaaa95ab7fe66935e3f7535413fad2a7d3">Volatility</a> <a class="el" href="class_quant_lib_1_1_local_vol_curve.html#aae14ca62291a64bc501d292224396525">localVolImpl</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">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#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>dummy</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [protected, virtual]</code></td>
</tr>
</table>
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<p>The relation </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \int_0^T \sigma_L^2(t)dt = \sigma_B^2 T \]" src="form_385.png"/>
</p>
<p> holds, where <img class="formulaInl" alt="$ \sigma_L(t) $" src="form_386.png"/> is the local volatility at time <img class="formulaInl" alt="$ t $" src="form_147.png"/> and <img class="formulaInl" alt="$ \sigma_B(T) $" src="form_387.png"/> is the Black volatility for maturity <img class="formulaInl" alt="$ T $" src="form_45.png"/>. From the above, the formula </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \sigma_L(t) = \sqrt{\frac{\mathrm{d}}{\mathrm{d}t}\sigma_B^2(t)t} \]" src="form_388.png"/>
</p>
<p> can be deduced which is here implemented. </p>
<p>Implements <a class="el" href="class_quant_lib_1_1_local_vol_term_structure.html#a0b539b6f4f12c8e2835533e11e593c95">LocalVolTermStructure</a>.</p>
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