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
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
|
<!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>OneFactorStudentCopula 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_one_factor_student_copula.html">OneFactorStudentCopula</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">OneFactorStudentCopula Class Reference</div> </div>
</div><!--header-->
<div class="contents">
<!-- doxytag: class="QuantLib::OneFactorStudentCopula" --><!-- doxytag: inherits="QuantLib::OneFactorCopula" -->
<p>One-factor Double Student t-Copula.
<a href="class_quant_lib_1_1_one_factor_student_copula.html#details">More...</a></p>
<p><code>#include <ql/experimental/credit/onefactorstudentcopula.hpp></code></p>
<div class="dynheader">
Inheritance diagram for OneFactorStudentCopula:</div>
<div class="dyncontent">
<div class="center"><img src="class_quant_lib_1_1_one_factor_student_copula__inherit__graph.png" border="0" usemap="#_one_factor_student_copula_inherit__map" alt="Inheritance graph"/></div>
<map name="_one_factor_student_copula_inherit__map" id="_one_factor_student_copula_inherit__map">
<area shape="rect" id="node2" href="class_quant_lib_1_1_one_factor_copula.html" title="Abstract base class for one-factor copula models." alt="" coords="28,6,151,37"/></map>
<center><span class="legend">[<a href="graph_legend.html">legend</a>]</span></center></div>
<p><a href="class_quant_lib_1_1_one_factor_student_copula-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="a890dd6482a39a580e3a2debe24cd55f1"></a><!-- doxytag: member="QuantLib::OneFactorStudentCopula::OneFactorStudentCopula" ref="a890dd6482a39a580e3a2debe24cd55f1" args="(const Handle< Quote > &correlation, int nz, int nm, Real maximum=10, Size integrationSteps=200)" -->
 </td><td class="memItemRight" valign="bottom"><b>OneFactorStudentCopula</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#ac63b6b972e9461ed9c0de2899f6fdc45">correlation</a>, int nz, int nm, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> maximum=10, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> integrationSteps=200)</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_one_factor_student_copula.html#a87748e5305096b30afeeaa93ce59137c">density</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> m) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Density function of M. <a href="#a87748e5305096b30afeeaa93ce59137c"></a><br/></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_one_factor_student_copula.html#a7f12eff80e70545a68af09aaab9a5bfa">cumulativeZ</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> z) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Cumulative distribution of Z. <a href="#a7f12eff80e70545a68af09aaab9a5bfa"></a><br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>One-factor Double Student t-Copula. </p>
<p>The copula model </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ Y_i = a_i\,M+\sqrt{1-a_i^2}\:Z_i \]" src="form_88.png"/>
</p>
<p>is specified here by setting the probability density functions for <img class="formulaInl" alt="$ Z_i $" src="form_120.png"/> ( <img class="formulaInl" alt="$ D_Z $" src="form_121.png"/>) and <img class="formulaInl" alt="$ M $" src="form_122.png"/> ( <img class="formulaInl" alt="$ D_M $" src="form_123.png"/>) to Student t-distributions with <img class="formulaInl" alt="$ N_z $" src="form_124.png"/> and <img class="formulaInl" alt="$ N_m $" src="form_125.png"/> degrees of freedom, respectively.</p>
<p>The variance of the Student t-distribution with <img class="formulaInl" alt="$ \nu $" src="form_126.png"/> degrees of freedom is <img class="formulaInl" alt="$ \nu / (\nu - 2) $" src="form_127.png"/>. Since the copula approach requires zero mean and unit variance distributions, variables <img class="formulaInl" alt="$ Z $" src="form_128.png"/> and <img class="formulaInl" alt="$ M $" src="form_122.png"/> are scaled by <img class="formulaInl" alt="$ \sqrt{(N_z - 2) / N_z} $" src="form_129.png"/> and <img class="formulaInl" alt="$ \sqrt{(N_m - 2) / N_m}, $" src="form_130.png"/> respectively.</p>
<dl class="todo"><dt><b><a class="el" href="todo.html#_todo000008">Possible enhancements:</a></b></dt><dd>Improve performance/accuracy of the calculation of inverse cumulative Y. Tabulate and store it for selected correlations? </dd></dl>
</div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a87748e5305096b30afeeaa93ce59137c"></a><!-- doxytag: member="QuantLib::OneFactorStudentCopula::density" ref="a87748e5305096b30afeeaa93ce59137c" args="(Real m) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_one_factor_student_copula.html#a87748e5305096b30afeeaa93ce59137c">density</a> </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<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Density function of M. </p>
<p>Derived classes must override this method and ensure zero mean and unit variance. </p>
<p>Implements <a class="el" href="class_quant_lib_1_1_one_factor_copula.html#a150d8a5373b942a7411cad42857ac0c2">OneFactorCopula</a>.</p>
</div>
</div>
<a class="anchor" id="a7f12eff80e70545a68af09aaab9a5bfa"></a><!-- doxytag: member="QuantLib::OneFactorStudentCopula::cumulativeZ" ref="a7f12eff80e70545a68af09aaab9a5bfa" args="(Real z) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_one_factor_student_copula.html#a7f12eff80e70545a68af09aaab9a5bfa">cumulativeZ</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>z</em></td><td>)</td>
<td> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Cumulative distribution of Z. </p>
<p>Derived classes must override this method and ensure zero mean and unit variance. </p>
<p>Implements <a class="el" href="class_quant_lib_1_1_one_factor_copula.html#a4d78de201751058a580a4104b569252f">OneFactorCopula</a>.</p>
</div>
</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>
|
