Statistical Inference and Pricing for Regime Switching Models in Finance and Insurance
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This thesis studies the estimation, goodness-of-fit testing, pricing and sampling problems for regime switching models, which are popularly used in financial markets. Specifically, we consider such models whose distributions are characterized by their characteristic functions, for example, Levy processes. The thesis contains the following contents: Chapter 1 introduces regime switching models and Levy processes. Then we present the problems we would like to address in the following chapters and our main contributions to these problems. Chapter 2 studies the estimation problem for regime switching Levy processes. We extend an existing estimation method that is based on characteristic functions to our models. Meanwhile, we compare the estimation results obtained by the proposed estimation method with those obtained by the expectation-maximization (EM) algorithm. We also address several computational challenges within the proposed estimation method. Chapter 3 studies the goodness-of-fit testing problem for regime switching models, where we extend two existing goodness-of-fit tests. Both of the proposed tests are based on characteristic functions. Chapter 4 applies the estimation and testing methods proposed in Chapters 2 and 3 to a set of S&P 500 real data. Chapter 5 studies the pricing problem for regime switching Levy processes. We propose a numerical pricing method that provides a unified pricing framework. The proposed method is illustrated by pricing European and Bermudan options and ratchet equity-index annuities (EIAs) with surrender risk. Chapter 6 studies the problem of sampling conditioned processes of regime switching models, where we propose an algorithm to sample paths from conditioned processes for a two-regime switching Black-Scholes model. Then we apply the proposed algorithm to the problems of pricing and static hedging of path-dependent options, where we use an Asian call option for illustrations. Chapter 7 lists several topics for future research.