Pricing of Bond Options: Unspanned Stochastic Volatility and Random Field Models

ISBN-13: 9783540707219 / Angielski / Miękka / 2008 / 148 str.

Detlef Repplinger

Opis

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.

Spis treści

The option pricing framework.- The Edgeworth Expansion.- The Integrated Edgeworth Expansion.- Multi-Factor HJM models.- Multiple-Random Fields term structure models.- Multi-factor USV term structure model.- Conclusions.- Matlab codes for the EE and IEE.

Blurb

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.