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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<a class="el" href="class_quant_lib_1_1_generic_risk_statistics.html">GenericRiskStatistics</a></div>
<h1>GenericRiskStatistics Class Template Reference</h1><!-- doxytag: class="QuantLib::GenericRiskStatistics" --><!-- doxytag: inherits="QuantLib::S" --><code>#include <ql/math/statistics/riskstatistics.hpp></code>
<p>
Inherits S.
<p>
<p>
<a href="class_quant_lib_1_1_generic_risk_statistics-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
<h3>template<class S><br>
class QuantLib::GenericRiskStatistics< S ></h3>
empirical-distribution risk measures
<p>
This class wraps a somewhat generic statistic tool and adds a number of risk measures (e.g.: value-at-risk, expected shortfall, etc.) based on the data distribution as reported by the underlying statistic tool.<p>
<dl compact><dt><b><a class="el" href="todo.html#_todo000027">Possible enhancements:</a></b></dt><dd>add historical annualized volatility</dd></dl>
<dl compact><dt><b>Examples: </b></dt><dd>
<p>
<a class="el" href="_discrete_hedging_8cpp-example.html#_a27">DiscreteHedging.cpp</a>.</dl><table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Types</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cec15026159cf469320e8a533d2a0bb7"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::value_type" ref="cec15026159cf469320e8a533d2a0bb7" args="" -->
typedef S::value_type </td><td class="memItemRight" valign="bottom"><b>value_type</b></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="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_generic_risk_statistics.html#1fc992d2d5933a547499c497d9e09b63">semiVariance</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><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_generic_risk_statistics.html#248a8283cddbe62eb1effbd5ee38a83a">semiDeviation</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><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_generic_risk_statistics.html#96208da819b87577a64a939239038fee">downsideVariance</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><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_generic_risk_statistics.html#0d6c0d73e07b78236d6b36bf17603783">downsideDeviation</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><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_generic_risk_statistics.html#f214276fcd65cb61f1213848bc37bcec">regret</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> target) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><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_generic_risk_statistics.html#7054629fa3befb2fe170756750fc05a5">potentialUpside</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> percentile) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">potential upside (the reciprocal of VAR) at a given percentile <a href="#7054629fa3befb2fe170756750fc05a5"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><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_generic_risk_statistics.html#53b553c9124491efa37dc8494453bc75">valueAtRisk</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> percentile) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">value-at-risk at a given percentile <a href="#53b553c9124491efa37dc8494453bc75"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><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_generic_risk_statistics.html#d8217a9c215c1fd0674ae4b4357fa035">expectedShortfall</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> percentile) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">expected shortfall at a given percentile <a href="#d8217a9c215c1fd0674ae4b4357fa035"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><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_generic_risk_statistics.html#ef5cddadc0fc859f9036eddb837a6ef0">shortfall</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> target) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><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_generic_risk_statistics.html#48f20722a46e929532f3fe29d05f38b9">averageShortfall</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> target) const </td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="1fc992d2d5933a547499c497d9e09b63"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::semiVariance" ref="1fc992d2d5933a547499c497d9e09b63" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> semiVariance </td>
<td>(</td>
<td class="paramname"> </td>
<td> ) </td>
<td width="100%"> const</td>
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</div>
<div class="memdoc">
<p>
returns the variance of observations below the mean, <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \frac{N}{N-1} \mathrm{E}\left[ (x-\langle x \rangle)^2 \;|\; x < \langle x \rangle \right]. \]" src="form_197.png">
<p>
<p>
See Markowitz (1959).
</div>
</div><p>
<a class="anchor" name="248a8283cddbe62eb1effbd5ee38a83a"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::semiDeviation" ref="248a8283cddbe62eb1effbd5ee38a83a" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> semiDeviation </td>
<td>(</td>
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<td> ) </td>
<td width="100%"> const</td>
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<div class="memdoc">
<p>
returns the semi deviation, defined as the square root of the semi variance.
</div>
</div><p>
<a class="anchor" name="96208da819b87577a64a939239038fee"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::downsideVariance" ref="96208da819b87577a64a939239038fee" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> downsideVariance </td>
<td>(</td>
<td class="paramname"> </td>
<td> ) </td>
<td width="100%"> const</td>
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<div class="memdoc">
<p>
returns the variance of observations below 0.0, <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \frac{N}{N-1} \mathrm{E}\left[ x^2 \;|\; x < 0\right]. \]" src="form_198.png">
<p>
</div>
</div><p>
<a class="anchor" name="0d6c0d73e07b78236d6b36bf17603783"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::downsideDeviation" ref="0d6c0d73e07b78236d6b36bf17603783" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> downsideDeviation </td>
<td>(</td>
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<td> ) </td>
<td width="100%"> const</td>
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<div class="memdoc">
<p>
returns the downside deviation, defined as the square root of the downside variance.
</div>
</div><p>
<a class="anchor" name="f214276fcd65cb61f1213848bc37bcec"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::regret" ref="f214276fcd65cb61f1213848bc37bcec" args="(Real target) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> regret </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>target</em> </td>
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<td width="100%"> const</td>
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<p>
returns the variance of observations below target, <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \frac{N}{N-1} \mathrm{E}\left[ (x-t)^2 \;|\; x < t \right]. \]" src="form_199.png">
<p>
<p>
See Dembo and Freeman, "The Rules Of Risk", Wiley (2001).
</div>
</div><p>
<a class="anchor" name="7054629fa3befb2fe170756750fc05a5"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::potentialUpside" ref="7054629fa3befb2fe170756750fc05a5" args="(Real percentile) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> potentialUpside </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>centile</em> </td>
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<td width="100%"> const</td>
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<p>
potential upside (the reciprocal of VAR) at a given percentile
<p>
<dl class="pre" compact><dt><b>Precondition:</b></dt><dd>percentile must be in range [90-100%) </dd></dl>
</div>
</div><p>
<a class="anchor" name="53b553c9124491efa37dc8494453bc75"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::valueAtRisk" ref="53b553c9124491efa37dc8494453bc75" args="(Real percentile) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> valueAtRisk </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>centile</em> </td>
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<p>
value-at-risk at a given percentile
<p>
<dl class="pre" compact><dt><b>Precondition:</b></dt><dd>percentile must be in range [90-100%) </dd></dl>
</div>
</div><p>
<a class="anchor" name="d8217a9c215c1fd0674ae4b4357fa035"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::expectedShortfall" ref="d8217a9c215c1fd0674ae4b4357fa035" args="(Real percentile) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> expectedShortfall </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>centile</em> </td>
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expected shortfall at a given percentile
<p>
returns the expected loss in case that the loss exceeded a VaR threshold,<p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathrm{E}\left[ x \;|\; x < \mathrm{VaR}(p) \right], \]" src="form_184.png">
<p>
<p>
that is the average of observations below the given percentile <img class="formulaInl" alt="$ p $" src="form_38.png">. Also know as conditional value-at-risk.<p>
See Artzner, Delbaen, Eber and Heath, "Coherent measures of risk", Mathematical Finance 9 (1999)<p>
<dl class="pre" compact><dt><b>Precondition:</b></dt><dd>percentile must be in range [90-100%) </dd></dl>
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<a class="anchor" name="ef5cddadc0fc859f9036eddb837a6ef0"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::shortfall" ref="ef5cddadc0fc859f9036eddb837a6ef0" args="(Real target) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> shortfall </td>
<td>(</td>
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probability of missing the given target, defined as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathrm{E}\left[ \Theta \;|\; (-\infty,\infty) \right] \]" src="form_200.png">
<p>
where <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \Theta(x) = \left\{ \begin{array}{ll} 1 & x < t \\ 0 & x \geq t \end{array} \right. \]" src="form_201.png">
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<a class="anchor" name="48f20722a46e929532f3fe29d05f38b9"></a><!-- doxytag: member="QuantLib::GenericRiskStatistics::averageShortfall" ref="48f20722a46e929532f3fe29d05f38b9" args="(Real target) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> averageShortfall </td>
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<p>
averaged shortfallness, defined as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathrm{E}\left[ t-x \;|\; x<t \right] \]" src="form_202.png">
<p>
</div>
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