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<!-- doxytag: class="QuantLib::SyntheticCDO" --><!-- doxytag: inherits="QuantLib::Instrument" -->
<p>Synthetic Collateralized Debt Obligation.
<a href="class_quant_lib_1_1_synthetic_c_d_o.html#details">More...</a></p>
<p><code>#include <ql/experimental/credit/syntheticcdo.hpp></code></p>
<div class="dynheader">
Inheritance diagram for SyntheticCDO:</div>
<div class="dyncontent">
<div class="center"><img src="class_quant_lib_1_1_synthetic_c_d_o__inherit__graph.png" border="0" usemap="#_synthetic_c_d_o_inherit__map" alt="Inheritance graph"/></div>
<map name="_synthetic_c_d_o_inherit__map" id="_synthetic_c_d_o_inherit__map">
<area shape="rect" id="node2" href="class_quant_lib_1_1_instrument.html" title="Abstract instrument class." alt="" coords="16,6,99,37"/></map>
<center><span class="legend">[<a href="graph_legend.html">legend</a>]</span></center></div>
<p><a href="class_quant_lib_1_1_synthetic_c_d_o-members.html">List of all members.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="nested-classes"></a>
Classes</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_synthetic_c_d_o_1_1engine.html">engine</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight"><a class="el" href="class_quant_lib_1_1_c_d_o.html" title="collateralized debt obligation">CDO</a> base engine. <a href="class_quant_lib_1_1_synthetic_c_d_o_1_1engine.html#details">More...</a><br/></td></tr>
<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="ab89b4f3cb58712bcfd1811c51191e43e"></a><!-- doxytag: member="QuantLib::SyntheticCDO::SyntheticCDO" ref="ab89b4f3cb58712bcfd1811c51191e43e" args="(const boost::shared_ptr< Basket > basket, Protection::Side side, const Schedule &schedule, Rate upfrontRate, Rate runningRate, const DayCounter &dayCounter, BusinessDayConvention paymentConvention, const Handle< YieldTermStructure > &yieldTS)" -->
 </td><td class="memItemRight" valign="bottom"><b>SyntheticCDO</b> (const boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_basket.html">Basket</a> > basket, Protection::Side side, const <a class="el" href="class_quant_lib_1_1_schedule.html">Schedule</a> &schedule, <a class="el" href="group__types.html#gaede435af51236692b1107d7639581d39">Rate</a> upfrontRate, <a class="el" href="group__types.html#gaede435af51236692b1107d7639581d39">Rate</a> runningRate, const <a class="el" href="class_quant_lib_1_1_day_counter.html">DayCounter</a> &dayCounter, <a class="el" href="group__datetime.html#gaff46c5ae9385d20709bedade86edd368">BusinessDayConvention</a> paymentConvention, const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_yield_term_structure.html">YieldTermStructure</a> > &yieldTS)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aea4975364ce04215976c4cecddba7261"></a><!-- doxytag: member="QuantLib::SyntheticCDO::basket" ref="aea4975364ce04215976c4cecddba7261" args="() const " -->
boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_basket.html">Basket</a> > </td><td class="memItemRight" valign="bottom"><b>basket</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a274c03751addc5c2ea63cc23d14a0bfe"></a><!-- doxytag: member="QuantLib::SyntheticCDO::isExpired" ref="a274c03751addc5c2ea63cc23d14a0bfe" args="() const " -->
bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_synthetic_c_d_o.html#a274c03751addc5c2ea63cc23d14a0bfe">isExpired</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns whether the instrument might have value greater than zero. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a439b4331763c1772af92bec6b182c62c"></a><!-- doxytag: member="QuantLib::SyntheticCDO::fairPremium" ref="a439b4331763c1772af92bec6b182c62c" args="() const " -->
<a class="el" href="group__types.html#gaede435af51236692b1107d7639581d39">Rate</a> </td><td class="memItemRight" valign="bottom"><b>fairPremium</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a9f9a340d55784f63ccfff9cf1979bd54"></a><!-- doxytag: member="QuantLib::SyntheticCDO::fairUpfrontPremium" ref="a9f9a340d55784f63ccfff9cf1979bd54" args="() const " -->
<a class="el" href="group__types.html#gaede435af51236692b1107d7639581d39">Rate</a> </td><td class="memItemRight" valign="bottom"><b>fairUpfrontPremium</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a8729d80e43b77566cbdf0cfe0b9b93dd"></a><!-- doxytag: member="QuantLib::SyntheticCDO::premiumValue" ref="a8729d80e43b77566cbdf0cfe0b9b93dd" args="() const " -->
<a class="el" href="group__types.html#gaede435af51236692b1107d7639581d39">Rate</a> </td><td class="memItemRight" valign="bottom"><b>premiumValue</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="abb77e8f956fe2e7458681bef8f73f9d0"></a><!-- doxytag: member="QuantLib::SyntheticCDO::protectionValue" ref="abb77e8f956fe2e7458681bef8f73f9d0" args="() const " -->
<a class="el" href="group__types.html#gaede435af51236692b1107d7639581d39">Rate</a> </td><td class="memItemRight" valign="bottom"><b>protectionValue</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a2f0a1cec9683f9dee08ad2ea12eda7aa"></a><!-- doxytag: member="QuantLib::SyntheticCDO::premiumLegNPV" ref="a2f0a1cec9683f9dee08ad2ea12eda7aa" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>premiumLegNPV</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a28658c93a5819086e55488a2a2e0e463"></a><!-- doxytag: member="QuantLib::SyntheticCDO::protectionLegNPV" ref="a28658c93a5819086e55488a2a2e0e463" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>protectionLegNPV</b> () const </td></tr>
<tr><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_synthetic_c_d_o.html#afb6649efb47dd3d59ef63002f3d27002">remainingNotional</a> () const </td></tr>
<tr><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_synthetic_c_d_o.html#a73193d76dd420560c91dbefc6874dd93">expectedTrancheLoss</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="afca3e3cf414a77cea53374f408cf8e0a"></a><!-- doxytag: member="QuantLib::SyntheticCDO::error" ref="afca3e3cf414a77cea53374f408cf8e0a" args="() const " -->
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>error</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_synthetic_c_d_o.html#aad6958108bfaef12bc4ccd6b3d7a7231">setupArguments</a> (PricingEngine::arguments *) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_synthetic_c_d_o.html#aa0a3105ddebcff9f233fb76a8a31fafe">fetchResults</a> (const PricingEngine::results *) const </td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Synthetic Collateralized Debt Obligation. </p>
<p>The instrument prices a mezzanine <a class="el" href="class_quant_lib_1_1_c_d_o.html" title="collateralized debt obligation">CDO</a> tranche with loss given default between attachment point <img class="formulaInl" alt="$ D_1$" src="form_66.png"/> and detachment point <img class="formulaInl" alt="$ D_2 > D_1 $" src="form_67.png"/>.</p>
<p>For purchased protection, the instrument value is given by the difference of the protection value <img class="formulaInl" alt="$ V_1 $" src="form_68.png"/> and premium value <img class="formulaInl" alt="$ V_2 $" src="form_69.png"/>,</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ V = V_1 - V_2. \]" src="form_70.png"/>
</p>
<p>The protection leg is priced as follows:</p>
<ul>
<li>Build the probability distribution for volume of defaults <img class="formulaInl" alt="$ L $" src="form_46.png"/> (before recovery) or Loss Given Default <img class="formulaInl" alt="$ LGD = (1-r)\,L $" src="form_71.png"/> at times/dates <img class="formulaInl" alt="$ t_i, i=1, ..., N$" src="form_72.png"/> (premium schedule times with intermediate steps)</li>
</ul>
<ul>
<li>Determine the expected value <img class="formulaInl" alt="$ E_i = E_{t_i}\,\left[Pay(LGD)\right] $" src="form_73.png"/> of the protection payoff <img class="formulaInl" alt="$ Pay(LGD) $" src="form_74.png"/> at each time <img class="formulaInl" alt="$ t_i$" src="form_75.png"/> where <p class="formulaDsp">
<img class="formulaDsp" alt="\[ Pay(L) = min (D_1, LGD) - min (D_2, LGD) = \left\{ \begin{array}{lcl} \displaystyle 0 &;& LGD < D_1 \\ \displaystyle LGD - D_1 &;& D_1 \leq LGD \leq D_2 \\ \displaystyle D_2 - D_1 &;& LGD > D_2 \end{array} \right. \]" src="form_76.png"/>
</p>
</li>
</ul>
<ul>
<li>The protection value is then calculated as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ V_1 \:=\: \sum_{i=1}^N (E_i - E_{i-1}) \cdot d_i \]" src="form_77.png"/>
</p>
where <img class="formulaInl" alt="$ d_i$" src="form_78.png"/> is the discount factor at time/date <img class="formulaInl" alt="$ t_i $" src="form_57.png"/></li>
</ul>
<p>The premium is paid on the protected notional amount, initially <img class="formulaInl" alt="$ D_2 - D_1. $" src="form_79.png"/> This notional amount is reduced by the expected protection payments <img class="formulaInl" alt="$ E_i $" src="form_80.png"/> at times <img class="formulaInl" alt="$ t_i, $" src="form_81.png"/> so that the premium value is calculated as</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ V_2 = m \, \cdot \sum_{i=1}^N \,(D_2 - D_1 - E_i) \cdot \Delta_{i-1,i}\,d_i \]" src="form_82.png"/>
</p>
<p>where <img class="formulaInl" alt="$ m $" src="form_39.png"/> is the premium rate, <img class="formulaInl" alt="$ \Delta_{i-1, i}$" src="form_83.png"/> is the day count fraction between date/time <img class="formulaInl" alt="$ t_{i-1}$" src="form_84.png"/> and <img class="formulaInl" alt="$ t_i.$" src="form_85.png"/></p>
<p>The construction of the portfolio loss distribution <img class="formulaInl" alt="$ E_i $" src="form_80.png"/> is based on the probability bucketing algorithm described in</p>
<p><b> John Hull and Alan White, "Valuation of a CDO and nth to default CDS
without Monte Carlo simulation", Journal of Derivatives 12, 2, 2004 </b></p>
<p>The pricing algorithm allows for varying notional amounts and default termstructures of the underlyings.</p>
<dl class="todo"><dt><b><a class="el" href="todo.html#_todo000011">Possible enhancements:</a></b></dt><dd>Investigate and fix cases <img class="formulaInl" alt="$ E_{i+1} < E_i. $" src="form_86.png"/> </dd></dl>
</div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="afb6649efb47dd3d59ef63002f3d27002"></a><!-- doxytag: member="QuantLib::SyntheticCDO::remainingNotional" ref="afb6649efb47dd3d59ef63002f3d27002" args="() const " -->
<div class="memitem">
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<tr>
<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_synthetic_c_d_o.html#afb6649efb47dd3d59ef63002f3d27002">remainingNotional</a> </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Total outstanding tranche notional, not wiped out </p>
</div>
</div>
<a class="anchor" id="a73193d76dd420560c91dbefc6874dd93"></a><!-- doxytag: member="QuantLib::SyntheticCDO::expectedTrancheLoss" ref="a73193d76dd420560c91dbefc6874dd93" args="() const " -->
<div class="memitem">
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<td class="memname">std::vector<<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>> <a class="el" href="class_quant_lib_1_1_synthetic_c_d_o.html#a73193d76dd420560c91dbefc6874dd93">expectedTrancheLoss</a> </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Expected tranche loss for all payment dates </p>
</div>
</div>
<a class="anchor" id="aad6958108bfaef12bc4ccd6b3d7a7231"></a><!-- doxytag: member="QuantLib::SyntheticCDO::setupArguments" ref="aad6958108bfaef12bc4ccd6b3d7a7231" args="(PricingEngine::arguments *) const " -->
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<td class="memname">void <a class="el" href="class_quant_lib_1_1_synthetic_c_d_o.html#aad6958108bfaef12bc4ccd6b3d7a7231">setupArguments</a> </td>
<td>(</td>
<td class="paramtype">PricingEngine::arguments * </td>
<td class="paramname"></td><td>)</td>
<td> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>When a derived argument structure is defined for an instrument, this method should be overridden to fill it. This is mandatory in case a pricing engine is used. </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_instrument.html#aad6958108bfaef12bc4ccd6b3d7a7231">Instrument</a>.</p>
</div>
</div>
<a class="anchor" id="aa0a3105ddebcff9f233fb76a8a31fafe"></a><!-- doxytag: member="QuantLib::SyntheticCDO::fetchResults" ref="aa0a3105ddebcff9f233fb76a8a31fafe" args="(const PricingEngine::results *) const " -->
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<td class="memname">void <a class="el" href="class_quant_lib_1_1_synthetic_c_d_o.html#aa0a3105ddebcff9f233fb76a8a31fafe">fetchResults</a> </td>
<td>(</td>
<td class="paramtype">const PricingEngine::results * </td>
<td class="paramname"><em>r</em></td><td>)</td>
<td> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>When a derived result structure is defined for an instrument, this method should be overridden to read from it. This is mandatory in case a pricing engine is used. </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_instrument.html#aa0a3105ddebcff9f233fb76a8a31fafe">Instrument</a>.</p>
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