Pricing models for Bermudan-style interest rate derivatives: Waarderingsmodellen voor Bermuda-stijl rente derivaten: proefschr..

Raoul Pietersz was born on 12 June 1978 in Rotterdam, The Netherlands. In 2000, he obtained a Certificate of Advanced Studies in Mathematics (Mathematical Tripos Part III), with distinction, from the University of Cambridge. Over the academic year 1999-2000, he was awarded a title of Cambridge European Trust Scholar, and a retrospective title of Scholar at Peterhouse, Cambridge. In the summer of 2000, he completed internships at UBS Warburg and Dresdner Kleinwort Wasserstein, in London. In 2001, he obtained a first class M.Sc. degree in Mathematics from Leiden University. His Master’s thesis entitled The LIBOR market modelʺwas completed during an internship at ABN AMRO Bank, in Amsterdam. Over the period 1997-2001, he was awarded the Shell International Scholarship for undergraduate studies. His Ph.D. research, under supervision of Antoon Pelsser and Ton Vorst, focuses on the efficient valuation and risk management of interest rate derivatives. He has published articles in The Journal of Computational Finance, The Journal of Derivatives, Quantitative Finance, Risk Magazine and Wilmott Magazine. He has presented his research at various international conferences. His teaching experience includes lecturing taught Master courses on derivatives at the Rotterdam School of Management. Since the start of the Ph.D. period, he has held a part-time position at ABN AMRO Bank, initially at Quantitative Risk Analytics, Risk Management. Since July 2004, he is a Senior Derivatives Researcher, developing front-office pricing models for interest rate derivatives, at Product Development Group, Quantitative Analytics, as part of Structured Derivatives. 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