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<li class="navelem"><a class="el" href="namespace_quant_lib.html">QuantLib</a></li><li class="navelem"><a class="el" href="class_quant_lib_1_1_one_factor_copula.html">OneFactorCopula</a></li> </ul>
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<a href="#pub-methods">Public Member Functions</a> |
<a href="#pro-methods">Protected Member Functions</a> |
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<div class="title">OneFactorCopula Class Reference<span class="mlabels"><span class="mlabel">abstract</span></span></div> </div>
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<p>Abstract base class for one-factor copula models.
<a href="class_quant_lib_1_1_one_factor_copula.html#details">More...</a></p>
<p><code>#include <ql/experimental/credit/onefactorcopula.hpp></code></p>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:af4fe1d014da6e427fc150e9b79864621"><td class="memItemLeft" align="right" valign="top"><a id="af4fe1d014da6e427fc150e9b79864621"></a>
 </td><td class="memItemRight" valign="bottom"><b>OneFactorCopula</b> (const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_quote.html">Quote</a> > &<a class="el" href="class_quant_lib_1_1_one_factor_copula.html#a57ec65a070e2520e50ea597d4b081dcf">correlation</a>, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> maximum=5.0, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> integrationSteps=50, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> minimum=-5.0)</td></tr>
<tr class="separator:af4fe1d014da6e427fc150e9b79864621"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a150d8a5373b942a7411cad42857ac0c2"><td class="memItemLeft" align="right" valign="top">virtual <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_one_factor_copula.html#a150d8a5373b942a7411cad42857ac0c2">density</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> m) const =0</td></tr>
<tr class="memdesc:a150d8a5373b942a7411cad42857ac0c2"><td class="mdescLeft"> </td><td class="mdescRight">Density function of M. <a href="class_quant_lib_1_1_one_factor_copula.html#a150d8a5373b942a7411cad42857ac0c2">More...</a><br /></td></tr>
<tr class="separator:a150d8a5373b942a7411cad42857ac0c2"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a4d78de201751058a580a4104b569252f"><td class="memItemLeft" align="right" valign="top">virtual <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_one_factor_copula.html#a4d78de201751058a580a4104b569252f">cumulativeZ</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> z) const =0</td></tr>
<tr class="memdesc:a4d78de201751058a580a4104b569252f"><td class="mdescLeft"> </td><td class="mdescRight">Cumulative distribution of Z. <a href="class_quant_lib_1_1_one_factor_copula.html#a4d78de201751058a580a4104b569252f">More...</a><br /></td></tr>
<tr class="separator:a4d78de201751058a580a4104b569252f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad3c053a659e9759ffad50358e17ced8e"><td class="memItemLeft" align="right" valign="top">virtual <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_one_factor_copula.html#ad3c053a659e9759ffad50358e17ced8e">cumulativeY</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> y) const</td></tr>
<tr class="memdesc:ad3c053a659e9759ffad50358e17ced8e"><td class="mdescLeft"> </td><td class="mdescRight">Cumulative distribution of Y. <a href="class_quant_lib_1_1_one_factor_copula.html#ad3c053a659e9759ffad50358e17ced8e">More...</a><br /></td></tr>
<tr class="separator:ad3c053a659e9759ffad50358e17ced8e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a6e27d7a3d32983317ff7b7f0ed19236d"><td class="memItemLeft" align="right" valign="top">virtual <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_one_factor_copula.html#a6e27d7a3d32983317ff7b7f0ed19236d">inverseCumulativeY</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> p) const</td></tr>
<tr class="memdesc:a6e27d7a3d32983317ff7b7f0ed19236d"><td class="mdescLeft"> </td><td class="mdescRight">Inverse cumulative distribution of Y. <a href="class_quant_lib_1_1_one_factor_copula.html#a6e27d7a3d32983317ff7b7f0ed19236d">More...</a><br /></td></tr>
<tr class="separator:a6e27d7a3d32983317ff7b7f0ed19236d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a57ec65a070e2520e50ea597d4b081dcf"><td class="memItemLeft" align="right" valign="top"><a id="a57ec65a070e2520e50ea597d4b081dcf"></a>
<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_one_factor_copula.html#a57ec65a070e2520e50ea597d4b081dcf">correlation</a> () const</td></tr>
<tr class="memdesc:a57ec65a070e2520e50ea597d4b081dcf"><td class="mdescLeft"> </td><td class="mdescRight">Single correlation parameter. <br /></td></tr>
<tr class="separator:a57ec65a070e2520e50ea597d4b081dcf"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a0173ef204d8fac41c6aa7b81b6d1912b"><td class="memItemLeft" align="right" valign="top"><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_one_factor_copula.html#a0173ef204d8fac41c6aa7b81b6d1912b">conditionalProbability</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> prob, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> m) const</td></tr>
<tr class="memdesc:a0173ef204d8fac41c6aa7b81b6d1912b"><td class="mdescLeft"> </td><td class="mdescRight">Conditional probability. <a href="class_quant_lib_1_1_one_factor_copula.html#a0173ef204d8fac41c6aa7b81b6d1912b">More...</a><br /></td></tr>
<tr class="separator:a0173ef204d8fac41c6aa7b81b6d1912b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a43a8acce4970917ba16132db55d0219d"><td class="memItemLeft" align="right" valign="top">std::vector< <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_one_factor_copula.html#a43a8acce4970917ba16132db55d0219d">conditionalProbability</a> (const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > &prob, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> m) const</td></tr>
<tr class="memdesc:a43a8acce4970917ba16132db55d0219d"><td class="mdescLeft"> </td><td class="mdescRight">Vector of conditional probabilities. <a href="class_quant_lib_1_1_one_factor_copula.html#a43a8acce4970917ba16132db55d0219d">More...</a><br /></td></tr>
<tr class="separator:a43a8acce4970917ba16132db55d0219d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a246c888ec75299856796aa24c9864349"><td class="memItemLeft" align="right" valign="top"><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_one_factor_copula.html#a246c888ec75299856796aa24c9864349">integral</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> p) const</td></tr>
<tr class="separator:a246c888ec75299856796aa24c9864349"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab1a16703dc782105c545b3e1f5262549"><td class="memTemplParams" colspan="2">template<class F > </td></tr>
<tr class="memitem:ab1a16703dc782105c545b3e1f5262549"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_one_factor_copula.html#ab1a16703dc782105c545b3e1f5262549">integral</a> (const F &f, std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > &probabilities) const</td></tr>
<tr class="separator:ab1a16703dc782105c545b3e1f5262549"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a4640097e612574bc0706e37171cb3b48"><td class="memTemplParams" colspan="2">template<class F > </td></tr>
<tr class="memitem:a4640097e612574bc0706e37171cb3b48"><td class="memTemplItemLeft" align="right" valign="top">Distribution </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_one_factor_copula.html#a4640097e612574bc0706e37171cb3b48">integral</a> (const F &f, const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > &nominals, const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > &probabilities) const</td></tr>
<tr class="separator:a4640097e612574bc0706e37171cb3b48"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad9319892fca9e4d916f3a655214ce84f"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_one_factor_copula.html#ad9319892fca9e4d916f3a655214ce84f">checkMoments</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> tolerance) const</td></tr>
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<tr class="inherit_header pub_methods_class_quant_lib_1_1_lazy_object"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_lazy_object')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_lazy_object.html">LazyObject</a></td></tr>
<tr class="memitem:ac5c54df7ed3b930268c8d7752c101725 inherit pub_methods_class_quant_lib_1_1_lazy_object"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_lazy_object.html#ac5c54df7ed3b930268c8d7752c101725">update</a> ()</td></tr>
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<tr class="memitem:a467a786be42a2165aa15a26709674547 inherit pub_methods_class_quant_lib_1_1_lazy_object"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_lazy_object.html#a467a786be42a2165aa15a26709674547">recalculate</a> ()</td></tr>
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<tr class="memitem:abd8698b462ce90fe56b15ce7a0192d3e inherit pub_methods_class_quant_lib_1_1_lazy_object"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_lazy_object.html#abd8698b462ce90fe56b15ce7a0192d3e">freeze</a> ()</td></tr>
<tr class="separator:abd8698b462ce90fe56b15ce7a0192d3e inherit pub_methods_class_quant_lib_1_1_lazy_object"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a26c02da24a82bc72024a8e8d48af0fca inherit pub_methods_class_quant_lib_1_1_lazy_object"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_lazy_object.html#a26c02da24a82bc72024a8e8d48af0fca">unfreeze</a> ()</td></tr>
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<tr class="memitem:a2ee394ca135f85485023ce3dc037149c inherit pub_methods_class_quant_lib_1_1_lazy_object"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_lazy_object.html#a2ee394ca135f85485023ce3dc037149c">alwaysForwardNotifications</a> ()</td></tr>
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<tr class="inherit_header pub_methods_class_quant_lib_1_1_observable"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_observable')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a></td></tr>
<tr class="memitem:a840dd96e33a304cbf681d357de7f48d0 inherit pub_methods_class_quant_lib_1_1_observable"><td class="memItemLeft" align="right" valign="top"><a id="a840dd96e33a304cbf681d357de7f48d0"></a>
 </td><td class="memItemRight" valign="bottom"><b>Observable</b> (const <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> &)</td></tr>
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<tr class="memitem:a522aacdd0f2408fe5e46527a6db999b4 inherit pub_methods_class_quant_lib_1_1_observable"><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_observable.html#a522aacdd0f2408fe5e46527a6db999b4">operator=</a> (const <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> &)</td></tr>
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<tr class="memitem:a397546715bfc5aedd1d16dd202a19d4c inherit pub_methods_class_quant_lib_1_1_observable"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_observable.html#a397546715bfc5aedd1d16dd202a19d4c">notifyObservers</a> ()</td></tr>
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<tr class="inherit_header pub_methods_class_quant_lib_1_1_observer"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_observer')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_observer.html">Observer</a></td></tr>
<tr class="memitem:af6a9d3ca0b7f388f3b7ccb1eccf11f63 inherit pub_methods_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top"><a id="af6a9d3ca0b7f388f3b7ccb1eccf11f63"></a>
 </td><td class="memItemRight" valign="bottom"><b>Observer</b> (const <a class="el" href="class_quant_lib_1_1_observer.html">Observer</a> &)</td></tr>
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<a class="el" href="class_quant_lib_1_1_observer.html">Observer</a> & </td><td class="memItemRight" valign="bottom"><b>operator=</b> (const <a class="el" href="class_quant_lib_1_1_observer.html">Observer</a> &)</td></tr>
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std::pair< iterator, bool > </td><td class="memItemRight" valign="bottom"><b>registerWith</b> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> > &)</td></tr>
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<tr class="memitem:a51d57eb97a3a57312a47bda29235f182 inherit pub_methods_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_observer.html#a51d57eb97a3a57312a47bda29235f182">registerWithObservables</a> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_observer.html">Observer</a> > &)</td></tr>
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<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>unregisterWith</b> (const ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> > &)</td></tr>
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void </td><td class="memItemRight" valign="bottom"><b>unregisterWithAll</b> ()</td></tr>
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<tr class="memitem:a3d53f9669c128dadc74a5d044a7c8e68 inherit pub_methods_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_observer.html#a3d53f9669c128dadc74a5d044a7c8e68">deepUpdate</a> ()</td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pro-methods"></a>
Protected Member Functions</h2></td></tr>
<tr class="memitem:ab9cc03f66a0444cc402d980b480b5211"><td class="memItemLeft" align="right" valign="top"><a id="ab9cc03f66a0444cc402d980b480b5211"></a>
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>steps</b> () const</td></tr>
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<tr class="memitem:a036d1d09c0c351638de1f0bf06c25ec2"><td class="memItemLeft" align="right" valign="top"><a id="a036d1d09c0c351638de1f0bf06c25ec2"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>dm</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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<tr class="memitem:a2fd7181876ebff2402b205087dedc5e6"><td class="memItemLeft" align="right" valign="top"><a id="a2fd7181876ebff2402b205087dedc5e6"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>m</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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<tr class="memitem:a650e16f4e7e68900d31d6c82a6d6a80a"><td class="memItemLeft" align="right" valign="top"><a id="a650e16f4e7e68900d31d6c82a6d6a80a"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>densitydm</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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<tr class="inherit_header pro_methods_class_quant_lib_1_1_lazy_object"><td colspan="2" onclick="javascript:toggleInherit('pro_methods_class_quant_lib_1_1_lazy_object')"><img src="closed.png" alt="-"/> Protected Member Functions inherited from <a class="el" href="class_quant_lib_1_1_lazy_object.html">LazyObject</a></td></tr>
<tr class="memitem:a082ff96da379d5e17436372ccb3c0972 inherit pro_methods_class_quant_lib_1_1_lazy_object"><td class="memItemLeft" align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_lazy_object.html#a082ff96da379d5e17436372ccb3c0972">calculate</a> () const</td></tr>
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<tr class="memitem:a572dbe926524786c64db01e31dba7ab8 inherit pro_methods_class_quant_lib_1_1_lazy_object"><td class="memItemLeft" align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_lazy_object.html#a572dbe926524786c64db01e31dba7ab8">performCalculations</a> () const =0</td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pro-attribs"></a>
Protected Attributes</h2></td></tr>
<tr class="memitem:a0bbb8459d54c70260f5dc06646c622fe"><td class="memItemLeft" align="right" valign="top"><a id="a0bbb8459d54c70260f5dc06646c622fe"></a>
<a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_quote.html">Quote</a> > </td><td class="memItemRight" valign="bottom"><b>correlation_</b></td></tr>
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<tr class="memitem:a5b014cf28588b976cafd9ef99bd90bdd"><td class="memItemLeft" align="right" valign="top"><a id="a5b014cf28588b976cafd9ef99bd90bdd"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>max_</b></td></tr>
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<tr class="memitem:ad193bceb88346d2755789a09afa91d86"><td class="memItemLeft" align="right" valign="top"><a id="ad193bceb88346d2755789a09afa91d86"></a>
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>steps_</b></td></tr>
<tr class="separator:ad193bceb88346d2755789a09afa91d86"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a0109cc1a8c0dd24c6bac204843ca21ce"><td class="memItemLeft" align="right" valign="top"><a id="a0109cc1a8c0dd24c6bac204843ca21ce"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>min_</b></td></tr>
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std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > </td><td class="memItemRight" valign="bottom"><b>y_</b></td></tr>
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<tr class="memitem:a6704dd8a7ed41ffcfd146c09c417b028"><td class="memItemLeft" align="right" valign="top"><a id="a6704dd8a7ed41ffcfd146c09c417b028"></a>
std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > </td><td class="memItemRight" valign="bottom"><b>cumulativeY_</b></td></tr>
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<tr class="inherit_header pro_attribs_class_quant_lib_1_1_lazy_object"><td colspan="2" onclick="javascript:toggleInherit('pro_attribs_class_quant_lib_1_1_lazy_object')"><img src="closed.png" alt="-"/> Protected Attributes inherited from <a class="el" href="class_quant_lib_1_1_lazy_object.html">LazyObject</a></td></tr>
<tr class="memitem:abcf8c3b096b3eea8688019abe7180471 inherit pro_attribs_class_quant_lib_1_1_lazy_object"><td class="memItemLeft" align="right" valign="top"><a id="abcf8c3b096b3eea8688019abe7180471"></a>
bool </td><td class="memItemRight" valign="bottom"><b>calculated_</b></td></tr>
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bool </td><td class="memItemRight" valign="bottom"><b>frozen_</b></td></tr>
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bool </td><td class="memItemRight" valign="bottom"><b>alwaysForward_</b></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="inherited"></a>
Additional Inherited Members</h2></td></tr>
<tr class="inherit_header pub_types_class_quant_lib_1_1_observer"><td colspan="2" onclick="javascript:toggleInherit('pub_types_class_quant_lib_1_1_observer')"><img src="closed.png" alt="-"/> Public Types inherited from <a class="el" href="class_quant_lib_1_1_observer.html">Observer</a></td></tr>
<tr class="memitem:a78de5f2b6bce96d718e3c18b9f52d67c inherit pub_types_class_quant_lib_1_1_observer"><td class="memItemLeft" align="right" valign="top"><a id="a78de5f2b6bce96d718e3c18b9f52d67c"></a>
typedef boost::unordered_set< ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_observable.html">Observable</a> > > </td><td class="memItemRight" valign="bottom"><b>set_type</b></td></tr>
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typedef set_type::iterator </td><td class="memItemRight" valign="bottom"><b>iterator</b></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Abstract base class for one-factor copula models. </p>
<p>Reference: John Hull and Alan White, The Perfect Copula, June 2006</p>
<p>Let \(Q_i(t)\) be the cumulative probability of default of counterparty i before time t.</p>
<p>In a one-factor model, consider random variables </p><p class="formulaDsp">
\[ Y_i = a_i\,M+\sqrt{1-a_i^2}\:Z_i \]
</p>
<p> where \(M\) and \(Z_i\) have independent zero-mean unit-variance distributions and \(-1\leq a_i \leq 1\). The correlation between \(Y_i\) and \(Y_j\) is then \(a_i a_j\).</p>
<p>Let \(F_Y(y)\) be the cumulative distribution function of \(Y_i\). \(y\) is mapped to \(t\) such that percentiles match, i.e. \(F_Y(y)=Q_i(t)\) or \(y=F_Y^{-1}(Q_i(t))\).</p>
<p>Now let \(F_Z(z)\) be the cumulated distribution function of \(Z_i\). For given realization of \(M\), this determines the distribution of \(y\): </p><p class="formulaDsp">
\[ Prob \,(Y_i < y|M) = F_Z \left( \frac{y-a_i\,M}{\sqrt{1-a_i^2}}\right) \qquad \mbox{or} \qquad Prob \,(t_i < t|M) = F_Z \left( \frac{F_Y^{-1}(Q_i(t))-a_i\,M} {\sqrt{1-a_i^2}} \right) \]
</p>
<p>The distribution functions of \( M, Z_i \) are specified in derived classes. The distribution function of \( Y \) is then given by the convolution </p><p class="formulaDsp">
\[ F_Y(y) = Prob\,(Y<y) = \int_{-\infty}^\infty\,\int_{-\infty}^{\infty}\: D_Z(z)\,D_M(m) \quad \Theta \left(y - a\,m - \sqrt{1-a^2}\,z\right)\,dm\,dz, \qquad \Theta (x) = \left\{ \begin{array}{ll} 1 & x \geq 0 \\ 0 & x < 0 \end{array}\right. \]
</p>
<p> where \( D_Z(z) \) and \( D_M(m) \) are the probability densities of \( Z\) and \( M, \) respectively.</p>
<p>This convolution can also be written </p><p class="formulaDsp">
\[ F(y) = Prob \,(Y < y) = \int_{-\infty}^\infty D_M(m)\,dm\: \int_{-\infty}^{g(y,a,m)} D_Z(z)\,dz, \qquad g(y,a,m) = \frac{y - a\cdot m}{\sqrt{1-a^2}}, \qquad a < 1 \]
</p>
<p>or</p>
<p class="formulaDsp">
\[ F(y) = Prob \,(Y < y) = \int_{-\infty}^\infty D_Z(z)\,dz\: \int_{-\infty}^{h(y,a,z)} D_M(m)\,dm, \qquad h(y,a,z) = \frac{y - \sqrt{1 - a^2}\cdot z}{a}, \qquad a > 0. \]
</p>
<p>In general, \( F_Y(y) \) needs to be computed numerically.</p>
</div><h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a150d8a5373b942a7411cad42857ac0c2">◆ </a></span>density()</h2>
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<td class="memname">virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> density </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>m</em></td><td>)</td>
<td> const</td>
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<p>Density function of M. </p>
<p>Derived classes must override this method and ensure zero mean and unit variance. </p>
<p>Implemented in <a class="el" href="class_quant_lib_1_1_one_factor_student_gaussian_copula.html#ac262f7adaf97c3a6fe821fa44a91f034">OneFactorStudentGaussianCopula</a>, <a class="el" href="class_quant_lib_1_1_one_factor_gaussian_student_copula.html#ac262f7adaf97c3a6fe821fa44a91f034">OneFactorGaussianStudentCopula</a>, <a class="el" href="class_quant_lib_1_1_one_factor_student_copula.html#ac262f7adaf97c3a6fe821fa44a91f034">OneFactorStudentCopula</a>, and <a class="el" href="class_quant_lib_1_1_one_factor_gaussian_copula.html#ac262f7adaf97c3a6fe821fa44a91f034">OneFactorGaussianCopula</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a4d78de201751058a580a4104b569252f">◆ </a></span>cumulativeZ()</h2>
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<td class="memname">virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> cumulativeZ </td>
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<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>z</em></td><td>)</td>
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<p>Cumulative distribution of Z. </p>
<p>Derived classes must override this method and ensure zero mean and unit variance. </p>
<p>Implemented in <a class="el" href="class_quant_lib_1_1_one_factor_student_gaussian_copula.html#aa0fd9108ef27f504594b5b6992492842">OneFactorStudentGaussianCopula</a>, <a class="el" href="class_quant_lib_1_1_one_factor_gaussian_student_copula.html#aa0fd9108ef27f504594b5b6992492842">OneFactorGaussianStudentCopula</a>, <a class="el" href="class_quant_lib_1_1_one_factor_student_copula.html#aa0fd9108ef27f504594b5b6992492842">OneFactorStudentCopula</a>, and <a class="el" href="class_quant_lib_1_1_one_factor_gaussian_copula.html#aa0fd9108ef27f504594b5b6992492842">OneFactorGaussianCopula</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ad3c053a659e9759ffad50358e17ced8e">◆ </a></span>cumulativeY()</h2>
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<td class="memname">virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> cumulativeY </td>
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<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>y</em></td><td>)</td>
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<p>Cumulative distribution of Y. </p>
<p>This is the default implementation based on tabulated data. The table needs to be filled by derived classes. If analytic calculation is feasible, this method can also be overridden. </p>
<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_one_factor_gaussian_copula.html#ae98c6cf137ea0199e0ae6f5a6de0db90">OneFactorGaussianCopula</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a6e27d7a3d32983317ff7b7f0ed19236d">◆ </a></span>inverseCumulativeY()</h2>
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<td class="memname">virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> inverseCumulativeY </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>p</em></td><td>)</td>
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<p>Inverse cumulative distribution of Y. </p>
<p>This is the default implementation based on tabulated data. The table needs to be filled by derived classes. If analytic calculation is feasible, this method can also be overridden. </p>
<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_one_factor_gaussian_copula.html#a6c17d8ad9b73fa0c2069ffda0f13cd2c">OneFactorGaussianCopula</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a0173ef204d8fac41c6aa7b81b6d1912b">◆ </a></span>conditionalProbability() <span class="overload">[1/2]</span></h2>
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<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> conditionalProbability </td>
<td>(</td>
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<td class="paramname"><em>prob</em>, </td>
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<td class="paramname"><em>m</em> </td>
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<p>Conditional probability. </p>
<p class="formulaDsp">
\[ \hat p(m) = F_Z \left( \frac{F_Y^{-1}(p)-a\,m}{\sqrt{1-a^2}}\right) \]
</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a43a8acce4970917ba16132db55d0219d">◆ </a></span>conditionalProbability() <span class="overload">[2/2]</span></h2>
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<td class="memname">std::vector<<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>> conditionalProbability </td>
<td>(</td>
<td class="paramtype">const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td>
<td class="paramname"><em>prob</em>, </td>
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<p>Vector of conditional probabilities. </p>
<p class="formulaDsp">
\[ \hat p_i(m) = F_Z \left( \frac{F_Y^{-1}(p_i)-a\,m}{\sqrt{1-a^2}} \right) \]
</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a246c888ec75299856796aa24c9864349">◆ </a></span>integral() <span class="overload">[1/3]</span></h2>
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<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> integral </td>
<td>(</td>
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<td class="paramname"><em>p</em></td><td>)</td>
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<p>Integral over the density \( \rho(m) \) of M and the conditional probability related to p:</p>
<p class="formulaDsp">
\[ \int_{-\infty}^\infty\,dm\,\rho(m)\, F_Z \left( \frac{F_Y^{-1}(p)-a\,m}{\sqrt{1-a^2}}\right) \]
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<h2 class="memtitle"><span class="permalink"><a href="#ab1a16703dc782105c545b3e1f5262549">◆ </a></span>integral() <span class="overload">[2/3]</span></h2>
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<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> integral </td>
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<p>Integral over the density \( \rho(m) \) of M and a one-dimensional function \( f \) of conditional probabilities related to the input vector of probabilities p:</p>
<p class="formulaDsp">
\[ \int_{-\infty}^\infty\,dm\,\rho(m)\, f (\hat p_1, \hat p_2, \dots, \hat p_N), \qquad \hat p_i (m) = F_Z \left( \frac{F_Y^{-1}(p_i)-a\,m}{\sqrt{1-a^2}} \right) \]
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<h2 class="memtitle"><span class="permalink"><a href="#a4640097e612574bc0706e37171cb3b48">◆ </a></span>integral() <span class="overload">[3/3]</span></h2>
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<td class="memname">Distribution integral </td>
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<td class="paramtype">const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td>
<td class="paramname"><em>nominals</em>, </td>
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<td></td>
<td class="paramtype">const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td>
<td class="paramname"><em>probabilities</em> </td>
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<p>Integral over the density \( \rho(m) \) of M and a multi-dimensional function \( f \) of conditional probabilities related to the input vector of probabilities p:</p>
<p class="formulaDsp">
\[ \int_{-\infty}^\infty\,dm\,\rho(m)\, f (\hat p_1, \hat p_2, \dots, \hat p_N), \qquad \hat p_i = F_Z \left( \frac{F_Y^{-1}(p_i)-a\,m}{\sqrt{1-a^2}}\right) \]
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<h2 class="memtitle"><span class="permalink"><a href="#ad9319892fca9e4d916f3a655214ce84f">◆ </a></span>checkMoments()</h2>
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<td class="memname">int checkMoments </td>
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<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>tolerance</em></td><td>)</td>
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<p>Check moments (unit norm, zero mean and unit variance) of the distributions of M, Z, and Y by numerically integrating the respective density. <a class="el" href="class_quant_lib_1_1_parameter.html" title="Base class for model arguments.">Parameter</a> tolerance is the maximum tolerable absolute error. </p>
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