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Pricing Models for Bermudan-style Interest Rate Derivatives

出版	ERIM, 2005
ISBN	90589209929789058920997
URL	http://books.google.com.hk/books?id=9XXJkQEACAAJ&hl=&source=gbs_api

註釋The purpose of this thesis is to further knowledge of efficient valuation and risk management of interest rate derivatives (mainly of Bermudan-style but other types are also included) by extending the theory on market models. The main pricing model for these derivatives is the LIBOR market model. It allows for efficient calibration to volatility and correlation. The most outstanding result of the thesis is the development of new market models, named CMS and generic market models (Chapter 7). We specify precisely when an arbitrary structure of forward rates is arbitrage-free at all possible (future) states of the model. Chapter 2 investigates various popular calibration choices for the LIBOR market model and their effect on the quality of risk sensitivities of Bermudan swaptions. Chapters 3 and 4 solve the same problem in two completely different ways. The problem is the so-called rank reduction of correlation matrices, and occurs as a key part of calibrating multi-factor market models to correlation. Chapter 3 presents a solution for rank reduction of correlation matrices, based on majorization, which is a general technique from optimization. Chapter 4 develops a solution for rank reduction of correlation matrices based on geometric programming, which is optimization over curved space (manifolds). Chapter 5 introduces a new discretization for the LIBOR market model, the Brownian bridge discretization. Chapter 6 presents novel empirical comparisons on the performance of models in terms of reduction of risk. In Chapter 7, new CMS and generic market models are developed, which allow for ease of volatility calibration for a whole new range of derivatives, such as fixed-maturity Bermudan swaptions and Bermudan CMS swaptions.