1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html;charset=UTF-8">
<meta name="robots" content="none">
<title>LossDistHomogeneous Class Reference</title>
<link rel="stylesheet" href="quantlib.css" type="text/css">
<link rel="stylesheet" href="print.css" type="text/css" media="print">
<link rel="shortcut icon" href="favicon.ico" type="image/x-icon">
<link rel="icon" href="favicon.ico" type="image/x-icon">
</head>
<body>
<div id="container">
<div id="header">
<img class="titleimage"
src="QL-title.jpg" width="185" height="50" border="0"
alt="QuantLib">
<br>
<h3 class="subtitle">A free/open-source library for quantitative finance</h3>
</div>
<div id="menu">
<h3 class="navbartitle">Version 1.2</h3>
<hr>
<h3 class="navbartitle">Getting started</h3>
<ul class="navbarlist">
<li class="navlink"><a href="index.html">Introduction</a></li>
<li class="navlink"><a href="where.html">Where to get QuantLib</a></li>
<li class="navlink"><a href="install.html">Installation</a></li>
<li class="navlink"><a href="config.html">Configuration</a></li>
<li class="navlink"><a href="usage.html">Usage</a></li>
<li class="navlink"><a href="history.html">Version history</a></li>
<li class="navlink"><a href="resources.html">Additional resources</a></li>
<li class="navlink"><a href="group.html">The QuantLib group</a></li>
<li class="navlink"><a href="license.html">Copyright and license</a></li>
</ul>
<hr>
<h3 class="navbartitle">Reference manual</h3>
<ul class="navbarlist">
<li class="navlink"><a href="modules.html">Modules</a></li>
<li class="navlink"><a href="hierarchy.html">Class Hierarchy</a></li>
<li class="navlink"><a href="annotated.html">Compound List</a></li>
<li class="navlink"><a href="files.html">File List</a></li>
<li class="navlink"><a href="functions.html">Compound Members</a></li>
<li class="navlink"><a href="globals.html">File Members</a></li>
<li class="navlink"><a href="todo.html">Todo List</a></li>
<li class="navlink"><a href="bug.html">Known Bugs</a></li>
<li class="navlink"><a href="caveats.html">Caveats</a></li>
<li class="navlink"><a href="test.html">Test Suite</a></li>
<li class="navlink"><a href="examples.html">Examples</a></li>
</ul>
</div>
<div id="content">
<!--Doxygen-generated content-->
<!-- Generated by Doxygen 1.7.6.1 -->
<div id="nav-path" class="navpath">
<ul>
<li class="navelem"><b>QuantLib</b> </li>
<li class="navelem"><a class="el" href="class_quant_lib_1_1_loss_dist_homogeneous.html">LossDistHomogeneous</a> </li>
</ul>
</div>
</div>
<div class="header">
<div class="summary">
<a href="#pub-methods">Public Member Functions</a> </div>
<div class="headertitle">
<div class="title">LossDistHomogeneous Class Reference</div> </div>
</div><!--header-->
<div class="contents">
<!-- doxytag: class="QuantLib::LossDistHomogeneous" --><!-- doxytag: inherits="QuantLib::LossDist" -->
<p>Loss Distribution for Homogeneous Pool.
<a href="class_quant_lib_1_1_loss_dist_homogeneous.html#details">More...</a></p>
<p><code>#include <ql/experimental/credit/lossdistribution.hpp></code></p>
<div class="dynheader">
Inheritance diagram for LossDistHomogeneous:</div>
<div class="dyncontent">
<div class="center"><img src="class_quant_lib_1_1_loss_dist_homogeneous__inherit__graph.png" border="0" usemap="#_loss_dist_homogeneous_inherit__map" alt="Inheritance graph"/></div>
<map name="_loss_dist_homogeneous_inherit__map" id="_loss_dist_homogeneous_inherit__map">
<area shape="rect" id="node2" href="class_quant_lib_1_1_loss_dist.html" title="Probability formulas and algorithms." alt="" coords="47,6,119,37"/></map>
<center><span class="legend">[<a href="graph_legend.html">legend</a>]</span></center></div>
<p><a href="class_quant_lib_1_1_loss_dist_homogeneous-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="a5ec68acd2980624a117e2f8a96d7e746"></a><!-- doxytag: member="QuantLib::LossDistHomogeneous::LossDistHomogeneous" ref="a5ec68acd2980624a117e2f8a96d7e746" args="(Size nBuckets, Real maximum, Real epsilon=1e-6)" -->
 </td><td class="memItemRight" valign="bottom"><b>LossDistHomogeneous</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> nBuckets, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> maximum, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> epsilon=1e-6)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ac7a0218af248413f6f7f2392473489e1"></a><!-- doxytag: member="QuantLib::LossDistHomogeneous::operator()" ref="ac7a0218af248413f6f7f2392473489e1" args="(Real volume, const std::vector< Real > &probabilities) const " -->
Distribution </td><td class="memItemRight" valign="bottom"><b>operator()</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> volume, const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > &probabilities) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a0c71a619a048f010109b9d01231394d8"></a><!-- doxytag: member="QuantLib::LossDistHomogeneous::operator()" ref="a0c71a619a048f010109b9d01231394d8" args="(const std::vector< Real > &volumes, const std::vector< Real > &probabilities) const " -->
Distribution </td><td class="memItemRight" valign="bottom"><b>operator()</b> (const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > &volumes, const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > &probabilities) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a01ac704c1d58d3c0b62457aebf7097c3"></a><!-- doxytag: member="QuantLib::LossDistHomogeneous::buckets" ref="a01ac704c1d58d3c0b62457aebf7097c3" args="() const " -->
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>buckets</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ad7e73faa199a16d3c9dc6a7a7295c295"></a><!-- doxytag: member="QuantLib::LossDistHomogeneous::maximum" ref="ad7e73faa199a16d3c9dc6a7a7295c295" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>maximum</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a9d78a687cf2a391198bb3cbc08bc06cb"></a><!-- doxytag: member="QuantLib::LossDistHomogeneous::size" ref="a9d78a687cf2a391198bb3cbc08bc06cb" args="() const " -->
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>size</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ae4b79402c64e9204eba66fbfcfa96172"></a><!-- doxytag: member="QuantLib::LossDistHomogeneous::volume" ref="ae4b79402c64e9204eba66fbfcfa96172" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>volume</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a0b3e8728cbc57b2d94c2d8ec7e5fd682"></a><!-- doxytag: member="QuantLib::LossDistHomogeneous::probability" ref="a0b3e8728cbc57b2d94c2d8ec7e5fd682" args="() const " -->
std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > </td><td class="memItemRight" valign="bottom"><b>probability</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a268bff8021c785b7195ce608f0f9df24"></a><!-- doxytag: member="QuantLib::LossDistHomogeneous::excessProbability" ref="a268bff8021c785b7195ce608f0f9df24" args="() const " -->
std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > </td><td class="memItemRight" valign="bottom"><b>excessProbability</b> () const </td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Loss Distribution for Homogeneous Pool. </p>
<p>Loss Distribution for Homogeneous Pool</p>
<p>Loss distribution for equal volumes but varying probabilities of default.</p>
<p>The method builds the exact loss distribution for a homogeneous pool of underlyings iteratively by computing the convolution of the given loss distribution with the "loss distribution" of an additional credit following</p>
<p>Xiaofong Ma, "Numerical Methods for the Valuation of Synthetic
Collateralized Debt Obligations", PhD Thesis, Graduate Department of Computer Science, University of Toronto, 2007 <a href="http://www.cs.toronto.edu/pub/reports/na/ma-07-phd.pdf">http://www.cs.toronto.edu/pub/reports/na/ma-07-phd.pdf</a> (formula 2.1)</p>
<p>avoiding numerical instability of the algorithm by</p>
<p>John Hull and Alan White, "Valuation of a CDO and nth to default CDS
without Monte Carlo simulation", Journal of Derivatives 12, 2, 2004 </p>
</div></div><!-- contents -->
</div>
<div class="footer">
<div class="endmatter">
Documentation generated by
<a href="http://www.doxygen.org">Doxygen</a> 1.7.6.1
</div>
</div>
</div>
</body>
</html>
|
