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
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
|
<!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>OneFactorGaussianCopula 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_gaussian_copula.html">OneFactorGaussianCopula</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">OneFactorGaussianCopula Class Reference</div> </div>
</div><!--header-->
<div class="contents">
<!-- doxytag: class="QuantLib::OneFactorGaussianCopula" --><!-- doxytag: inherits="QuantLib::OneFactorCopula" -->
<p>One-factor Gaussian Copula.
<a href="class_quant_lib_1_1_one_factor_gaussian_copula.html#details">More...</a></p>
<p><code>#include <ql/experimental/credit/onefactorgaussiancopula.hpp></code></p>
<div class="dynheader">
Inheritance diagram for OneFactorGaussianCopula:</div>
<div class="dyncontent">
<div class="center"><img src="class_quant_lib_1_1_one_factor_gaussian_copula__inherit__graph.png" border="0" usemap="#_one_factor_gaussian_copula_inherit__map" alt="Inheritance graph"/></div>
<map name="_one_factor_gaussian_copula_inherit__map" id="_one_factor_gaussian_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="33,6,156,37"/></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_gaussian_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="ac697b3db3dc86d5b69db61a44191af4f"></a><!-- doxytag: member="QuantLib::OneFactorGaussianCopula::OneFactorGaussianCopula" ref="ac697b3db3dc86d5b69db61a44191af4f" args="(const Handle< Quote > &correlation, Real maximum=5, Size integrationSteps=50)" -->
 </td><td class="memItemRight" valign="bottom"><b>OneFactorGaussianCopula</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>, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> maximum=5, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> integrationSteps=50)</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_gaussian_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_gaussian_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>
<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_gaussian_copula.html#a712150bf4c40b6443a311f2569117760">cumulativeY</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> y) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a6d7feb2a05b8754fe0a79ff0f26b704e"></a><!-- doxytag: member="QuantLib::OneFactorGaussianCopula::testCumulativeY" ref="a6d7feb2a05b8754fe0a79ff0f26b704e" args="(Real y) const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>testCumulativeY</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> y) 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_one_factor_gaussian_copula.html#a309f9b6f2c8476ddc7d4d750a0f7d75c">inverseCumulativeY</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> p) const </td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>One-factor Gaussian 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 desnity function for all variables, <img class="formulaInl" alt="$ M, Z,$" src="form_118.png"/> and also <img class="formulaInl" alt="$ Y $" src="form_103.png"/> to the standard normal distribution <img class="formulaInl" alt="$ \phi(x) = \exp(-x^2/2) / \sqrt{2\pi}. $" src="form_119.png"/> </p>
</div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a87748e5305096b30afeeaa93ce59137c"></a><!-- doxytag: member="QuantLib::OneFactorGaussianCopula::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_gaussian_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::OneFactorGaussianCopula::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_gaussian_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>
<a class="anchor" id="a712150bf4c40b6443a311f2569117760"></a><!-- doxytag: member="QuantLib::OneFactorGaussianCopula::cumulativeY" ref="a712150bf4c40b6443a311f2569117760" args="(Real y) 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_gaussian_copula.html#a712150bf4c40b6443a311f2569117760">cumulativeY</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>y</em></td><td>)</td>
<td> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>overrides the base class implementation based on table data </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_one_factor_copula.html#aa5a31f6c22dc65de5eefc911e33d230e">OneFactorCopula</a>.</p>
</div>
</div>
<a class="anchor" id="a309f9b6f2c8476ddc7d4d750a0f7d75c"></a><!-- doxytag: member="QuantLib::OneFactorGaussianCopula::inverseCumulativeY" ref="a309f9b6f2c8476ddc7d4d750a0f7d75c" args="(Real p) 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_gaussian_copula.html#a309f9b6f2c8476ddc7d4d750a0f7d75c">inverseCumulativeY</a> </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>
<td> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>overrides the base class implementation based on table data </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_one_factor_copula.html#a37961e30f2d8786a4e4e6d1ef65516ed">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>
|
