Repplinger Pricing of Bond Options

Unspanned Stochastic Volatility and Random Field Models
1. Auflage 2008
ISBN: 978-3-540-70729-5
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 615, 138 Seiten

Reihe: Lecture Notes in Economics and Mathematical Systems

A major theme of this book is the development of a consistent unified model framework for the evaluation of bond options. In general options on zero bonds (e.g. caps) and options on coupon bearing bonds (e.g. swaptions) are linked by no-arbitrage relations through the correlation structure of interest rates. Therefore, unspanned stochastic volatility (USV) as well as Random Field (RF) models are used to model the dynamics of entire yield curves. The USV models postulate a correlation between the bond price dynamics and the subordinated stochastic volatility process, whereas Random Field models allow for a deterministic correlation structure between bond prices of different terms. Then the pricing of bond options is done either by running a Fractional Fourier Transform or by applying the Integrated Edgeworth Expansion approach. The latter is a new extension of a generalized series expansion of the (log) characteristic function, especially adapted for the computation of exercise probabilities.

Autoren/Hrsg.

Repplinger, Detlef

Inhaltsverzeichnis

1;Foreword;5
2;Acknowledgements;6
3;Contents;7
4;Introduction;9
5;The option pricing framework;14
5.1;2.1 Zero-coupon bond options;15
5.2;2.2 Coupon bond options;17
6;The Edgeworth Expansion;21
6.1;3.1 The generalized EE scheme;22
6.2;3.2 The approximation of a .2v -pdf;27
6.3;3.3 The approximation of a lognormal-pdf;30
7;The Integrated Edgeworth Expansion;35
7.1;4.1 The generalized IEE scheme;36
7.2;4.2 An approximation of the .2v -cdf;38
7.3;4.3 An approximation of the lognormal-cdf;40
8;Multi-Factor HJM models;45
8.1;5.1 The change of measure;49
8.2;5.2 Pricing of zero-coupon bond options;50
8.3;5.3 Pricing of coupon bond options;59
9;Multiple-Random Fields term structure models;76
9.1;6.1 Random Fields;76
9.2;6.2 Multiple-Random Field HJM-framework;80
9.3;6.3 Change of measure;85
9.4;6.4 Pricing of zero bond options;86
9.5;6.5 Pricing of coupon bond options;91
10;Multi-factor USV term structure model;98
10.1;7.1 The change of measure;102
10.2;7.2 Pricing of zero-coupon bond options;103
10.3;7.3 Pricing of coupon bond options;111
11;Conclusions;118
12;Appendix;122
12.1;9.1 Independent Brownian motions;122
12.2;9.2 Dependent Brownian motions;124
13;Matlab codes for the EE and IEE;129
13.1;10.1 Integer equation;129
13.2;10.2 Computation of the cumulants given the moments;130
13.3;10.3 Computation of the Hermite polynomial;131
13.4;10.4 The EE;132
13.5;10.5 The IEE;133
14;References;135
15;List of figures;139
16;List of tables;141