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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_black_formula.html">BlackFormula</a></div>
<h1>BlackFormula Class Reference</h1><!-- doxytag: class="QuantLib::BlackFormula" --><code>#include <ql/PricingEngines/blackformula.hpp></code>
<p>
<a href="class_quant_lib_1_1_black_formula-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Black-formula calculator.
<p>
<dl compact><dt><b><a class="el" href="bug.html#_bug000002">Bug:</a></b></dt><dd>When the variance is null, division by zero occur during the calculation of delta, delta forward, gamma, gamma forward, rho, dividend rho, vega, and strike sensitivity. </dd></dl>
<dl compact><dt><b>Examples: </b></dt><dd>
<p>
<a class="el" href="_discrete_hedging_8cpp-example.html#_a7">DiscreteHedging.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="316efeeb86bf42358f589fa1a5c41895"></a><!-- doxytag: member="QuantLib::BlackFormula::BlackFormula" ref="316efeeb86bf42358f589fa1a5c41895" args="(Real forward, DiscountFactor discount, Real variance, const boost::shared_ptr< StrikedTypePayoff > &payoff)" -->
</td><td class="memItemRight" valign="bottom"><b>BlackFormula</b> (Real forward, <a class="el" href="group__types.html#g642a971a0bcbbd2fb26c35e1a06e5761">DiscountFactor</a> discount, Real variance, const boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_striked_type_payoff.html">StrikedTypePayoff</a> > &payoff)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="72887400b9a4d1ba185b887b84876cdc"></a><!-- doxytag: member="QuantLib::BlackFormula::value" ref="72887400b9a4d1ba185b887b84876cdc" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>value</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1ce2edf271b7df5907ea9a3b100383fe"></a><!-- doxytag: member="QuantLib::BlackFormula::delta" ref="1ce2edf271b7df5907ea9a3b100383fe" args="(Real spot) const" -->
Real </td><td class="memItemRight" valign="bottom"><b>delta</b> (Real spot) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b6f8af630290d3010bc3bfc64304aa03"></a><!-- doxytag: member="QuantLib::BlackFormula::elasticity" ref="b6f8af630290d3010bc3bfc64304aa03" args="(Real spot) const" -->
Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_black_formula.html#b6f8af630290d3010bc3bfc64304aa03">elasticity</a> (Real spot) const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Sensitivity in percent to a percent movement in the underlying. <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="57565309e7b2cbfe856209958c63cfa5"></a><!-- doxytag: member="QuantLib::BlackFormula::gamma" ref="57565309e7b2cbfe856209958c63cfa5" args="(Real spot) const" -->
Real </td><td class="memItemRight" valign="bottom"><b>gamma</b> (Real spot) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d1aeee7c18b44d616b3c8169ebb9611a"></a><!-- doxytag: member="QuantLib::BlackFormula::deltaForward" ref="d1aeee7c18b44d616b3c8169ebb9611a" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>deltaForward</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7c544e51336c33f06b0a9158a3d2705e"></a><!-- doxytag: member="QuantLib::BlackFormula::elasticityForward" ref="7c544e51336c33f06b0a9158a3d2705e" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_black_formula.html#7c544e51336c33f06b0a9158a3d2705e">elasticityForward</a> () const</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Sensitivity in percent to a percent movement in the forward price. <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6949781d9c6ffe5419b5e463622430c6"></a><!-- doxytag: member="QuantLib::BlackFormula::gammaForward" ref="6949781d9c6ffe5419b5e463622430c6" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>gammaForward</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f7afb7a0e83603b71da76cd8923a07a2"></a><!-- doxytag: member="QuantLib::BlackFormula::theta" ref="f7afb7a0e83603b71da76cd8923a07a2" args="(Real spot, Time maturity) const" -->
Real </td><td class="memItemRight" valign="bottom"><b>theta</b> (Real spot, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> maturity) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bba1bf8797f099026e699408878caedc"></a><!-- doxytag: member="QuantLib::BlackFormula::thetaPerDay" ref="bba1bf8797f099026e699408878caedc" args="(Real spot, Time maturity) const" -->
Real </td><td class="memItemRight" valign="bottom"><b>thetaPerDay</b> (Real spot, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> maturity) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0c37734c53fa52703c6f0d22677b05ed"></a><!-- doxytag: member="QuantLib::BlackFormula::vega" ref="0c37734c53fa52703c6f0d22677b05ed" args="(Time maturity) const " -->
Real </td><td class="memItemRight" valign="bottom"><b>vega</b> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> maturity) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ffcfd1c0fd1c6bef1bb21fd2a336bff5"></a><!-- doxytag: member="QuantLib::BlackFormula::rho" ref="ffcfd1c0fd1c6bef1bb21fd2a336bff5" args="(Time maturity) const " -->
Real </td><td class="memItemRight" valign="bottom"><b>rho</b> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> maturity) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b880a4d01e68c373077c2c6cf68af259"></a><!-- doxytag: member="QuantLib::BlackFormula::dividendRho" ref="b880a4d01e68c373077c2c6cf68af259" args="(Time maturity) const " -->
Real </td><td class="memItemRight" valign="bottom"><b>dividendRho</b> (<a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> maturity) 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_black_formula.html#52f0d80c352ce23b6009d89a828b7824">itmCashProbability</a> () 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_black_formula.html#a0b200c24392e9cef0c2c467a925f290">itmAssetProbability</a> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="55b21c7d22a7fdce4611b3b95effc896"></a><!-- doxytag: member="QuantLib::BlackFormula::strikeSensitivity" ref="55b21c7d22a7fdce4611b3b95effc896" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>strikeSensitivity</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d7530134b03a24df85bd5ffe06507e87"></a><!-- doxytag: member="QuantLib::BlackFormula::alpha" ref="d7530134b03a24df85bd5ffe06507e87" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>alpha</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d50765ca99bba93b755d16557de7ad55"></a><!-- doxytag: member="QuantLib::BlackFormula::beta" ref="d50765ca99bba93b755d16557de7ad55" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>beta</b> () const</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="badcb24a4a0b52860a5e7618e3f66914"></a><!-- doxytag: member="QuantLib::BlackFormula::Calculator" ref="badcb24a4a0b52860a5e7618e3f66914" args="" -->
class </td><td class="memItemRight" valign="bottom"><b>Calculator</b></td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="52f0d80c352ce23b6009d89a828b7824"></a><!-- doxytag: member="QuantLib::BlackFormula::itmCashProbability" ref="52f0d80c352ce23b6009d89a828b7824" args="() const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname">Real itmCashProbability </td>
<td>(</td>
<td class="paramname"> </td>
<td> ) </td>
<td width="100%"> const</td>
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</table>
</div>
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<p>
Probability of being in the money in the bond martingale measure. It is a risk-neutral probability, not the real world probability.
</div>
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<a class="anchor" name="a0b200c24392e9cef0c2c467a925f290"></a><!-- doxytag: member="QuantLib::BlackFormula::itmAssetProbability" ref="a0b200c24392e9cef0c2c467a925f290" args="() const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname">Real itmAssetProbability </td>
<td>(</td>
<td class="paramname"> </td>
<td> ) </td>
<td width="100%"> const</td>
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</div>
<div class="memdoc">
<p>
Probability of being in the money in the asset martingale measure. It is a risk-neutral probability, not the real world probability.
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