Abstract zu Option Pricing in a Regime Switching Jump Diffusion Model
Title: Option Pricing in a Regime Switching Jump Diffusion Model
Abstract: In this talk I will consider a regime-switching jump diffusion model for the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure jump process, driving the values of interest rate and volatility coefficient. The pure jump process is assumed to be a semi-Markov process on finite state space. This consideration helps to incorporate a specific type of memory influence in the asset price. Under this model assumption, the locally risk minimizing prices of the European type path-independent options would be investigated. The F\"{o}llmer-Schweizer decomposition is adopted to show that the option price satisfies an evolution problem, as a function of time, stock price, market regime, and the stagnancy period. To be more precise, the evolution problem involves a linear, parabolic, degenerate and non-local system of integro-partial differential equations. We would also discuss a self-contained proof of existence and uniqueness of the classical solution to the evolution problem in the class of functions of at most linear growth.