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
|
<!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>HullWhite 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_hull_white.html">HullWhite</a> </li>
</ul>
</div>
</div>
<div class="header">
<div class="summary">
<a href="#nested-classes">Classes</a> |
<a href="#pub-methods">Public Member Functions</a> |
<a href="#pub-static-methods">Static Public Member Functions</a> |
<a href="#pro-methods">Protected Member Functions</a> </div>
<div class="headertitle">
<div class="title">HullWhite Class Reference<div class="ingroups"><a class="el" href="group__shortrate.html">Short-rate modelling framework</a></div></div> </div>
</div><!--header-->
<div class="contents">
<!-- doxytag: class="QuantLib::HullWhite" --><!-- doxytag: inherits="QuantLib::Vasicek,QuantLib::TermStructureConsistentModel" -->
<p>Single-factor Hull-White (extended Vasicek) model class.
<a href="class_quant_lib_1_1_hull_white.html#details">More...</a></p>
<p><code>#include <ql/models/shortrate/onefactormodels/hullwhite.hpp></code></p>
<div class="dynheader">
Inheritance diagram for HullWhite:</div>
<div class="dyncontent">
<div class="center"><img src="class_quant_lib_1_1_hull_white__inherit__graph.png" border="0" usemap="#_hull_white_inherit__map" alt="Inheritance graph"/></div>
<map name="_hull_white_inherit__map" id="_hull_white_inherit__map">
<area shape="rect" id="node2" href="class_quant_lib_1_1_vasicek.html" title="Vasicek model class" alt="" coords="5,6,72,37"/><area shape="rect" id="node4" href="class_quant_lib_1_1_term_structure_consistent_model.html" title="Term-structure consistent model class." alt="" coords="96,6,296,37"/></map>
<center><span class="legend">[<a href="graph_legend.html">legend</a>]</span></center></div>
<p><a href="class_quant_lib_1_1_hull_white-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_hull_white_1_1_dynamics.html">Dynamics</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Short-rate dynamics in the Hull-White model. <a href="class_quant_lib_1_1_hull_white_1_1_dynamics.html#details">More...</a><br/></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_hull_white_1_1_fitting_parameter.html">FittingParameter</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Analytical term-structure fitting parameter <img class="formulaInl" alt="$ \varphi(t) $" src="form_294.png"/>. <a href="class_quant_lib_1_1_hull_white_1_1_fitting_parameter.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="a5a576c1761c7ea4da9bb03a78b7ad5d5"></a><!-- doxytag: member="QuantLib::HullWhite::HullWhite" ref="a5a576c1761c7ea4da9bb03a78b7ad5d5" args="(const Handle< YieldTermStructure > &termStructure, Real a=0.1, Real sigma=0.01)" -->
 </td><td class="memItemRight" valign="bottom"><b>HullWhite</b> (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> > &termStructure, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> a=0.1, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> sigma=0.01)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a14130554fc69efb397b13bff53cc5eeb"></a><!-- doxytag: member="QuantLib::HullWhite::tree" ref="a14130554fc69efb397b13bff53cc5eeb" args="(const TimeGrid &grid) const " -->
boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_lattice.html">Lattice</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white.html#a14130554fc69efb397b13bff53cc5eeb">tree</a> (const <a class="el" href="class_quant_lib_1_1_time_grid.html">TimeGrid</a> &grid) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Return by default a trinomial recombining tree. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ab819304423e7791547c3089322a190be"></a><!-- doxytag: member="QuantLib::HullWhite::dynamics" ref="ab819304423e7791547c3089322a190be" args="() const " -->
boost::shared_ptr<br class="typebreak"/>
< <a class="el" href="class_quant_lib_1_1_one_factor_model_1_1_short_rate_dynamics.html">ShortRateDynamics</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white.html#ab819304423e7791547c3089322a190be">dynamics</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the short-rate dynamics <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a0b47448ed1ba48ac5138854aed3f1d49"></a><!-- doxytag: member="QuantLib::HullWhite::discountBondOption" ref="a0b47448ed1ba48ac5138854aed3f1d49" args="(Option::Type type, Real strike, Time maturity, Time bondMaturity) const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>discountBondOption</b> (Option::Type type, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> strike, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> maturity, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> bondMaturity) const </td></tr>
<tr><td colspan="2"><h2><a name="pub-static-methods"></a>
Static Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">static <a class="el" href="group__types.html#gaede435af51236692b1107d7639581d39">Rate</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_hull_white.html#af554e020436a6a21568f1149d61e2f54">convexityBias</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> futurePrice, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> T, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> sigma, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> a)</td></tr>
<tr><td colspan="2"><h2><a name="pro-methods"></a>
Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a4d8a7e8e132cf1dd8d1d9eac02f2bfae"></a><!-- doxytag: member="QuantLib::HullWhite::generateArguments" ref="a4d8a7e8e132cf1dd8d1d9eac02f2bfae" args="()" -->
void </td><td class="memItemRight" valign="bottom"><b>generateArguments</b> ()</td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a01dd11c13189fcd655784ccec798c410"></a><!-- doxytag: member="QuantLib::HullWhite::A" ref="a01dd11c13189fcd655784ccec798c410" args="(Time t, Time T) const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>A</b> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> T) const </td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Single-factor Hull-White (extended Vasicek) model class. </p>
<p>This class implements the standard single-factor Hull-White model defined by </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ dr_t = (\theta(t) - \alpha r_t)dt + \sigma dW_t \]" src="form_304.png"/>
</p>
<p> where <img class="formulaInl" alt="$ \alpha $" src="form_3.png"/> and <img class="formulaInl" alt="$ \sigma $" src="form_4.png"/> are constants.</p>
<dl class="test"><dt><b><a class="el" href="test.html#_test000084">Tests:</a></b></dt><dd>calibration results are tested against cached values</dd></dl>
<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000009">Bug:</a></b></dt><dd>When the term structure is relinked, the r0 parameter of the underlying <a class="el" href="class_quant_lib_1_1_vasicek.html" title="Vasicek model class">Vasicek</a> model is not updated.</dd></dl>
<dl><dt><b>Examples: </b></dt><dd><a class="el" href="_bermudan_swaption_8cpp-example.html#_a32">BermudanSwaption.cpp</a>, and <a class="el" href="_callable_bonds_8cpp-example.html#_a24">CallableBonds.cpp</a>.</dd>
</dl></div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="af554e020436a6a21568f1149d61e2f54"></a><!-- doxytag: member="QuantLib::HullWhite::convexityBias" ref="af554e020436a6a21568f1149d61e2f54" args="(Real futurePrice, Time t, Time T, Real sigma, Real a)" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">static <a class="el" href="group__types.html#gaede435af51236692b1107d7639581d39">Rate</a> <a class="el" href="class_quant_lib_1_1_hull_white.html#af554e020436a6a21568f1149d61e2f54">convexityBias</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>futurePrice</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>t</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>T</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>sigma</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>a</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td><code> [static]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Futures convexity bias (i.e., the difference between futures implied rate and forward rate) calculated as in G. Kirikos, D. Novak, "Convexity Conundrums", Risk Magazine, March 1997.</p>
<dl class="note"><dt><b>Note:</b></dt><dd>t and T should be expressed in yearfraction using deposit day counter, F_quoted is futures' market price. </dd></dl>
</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>
|
