Pricing of Bond Options
Unspanned Stochastic Volatility and Random Field Models
E-Book
Pricing of Bond Options
Unspanned Stochastic Volatility and Random Field Models
RWT Award 2008!
For his excellent monograph, Detlef Repplinger won the RWT Reutlinger Wirtschaftstreuhand GMBH award in June 2008.
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.
For his excellent monograph, Detlef Repplinger won the RWT Reutlinger Wirtschaftstreuhand GMBH award in June 2008.
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.
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
Repplinger, Detlef
| ISBN | 9783540707295 |
|---|---|
| Artikelnummer | 9783540707295 |
| Medientyp | E-Book - PDF |
| Auflage | 2. Aufl. |
| Copyrightjahr | 2008 |
| Verlag | Springer-Verlag |
| Umfang | 138 Seiten |
| Sprache | Englisch |
| Kopierschutz | Digitales Wasserzeichen |
