Degree Name

Doctor of Philosophy


School of Mathematics and Applied Statistics


Classified by different purposes and contributions, this thesis is divided into three parts. In specific, Part 1 focuses on different option pricing models with analytical pricing formula for European options, and three topics covered by the first part are 1) a new closed-form pricing formula is obtained under a skew Brownian motion; 2) an analytical approximation formula is derived when regime-switching is introduced into the Heston model; and 3) a modified black-scholes option pricing formula is presented when the underlying price is bounded. Part 2 is devoted to solving option pricing problems with different solution techniques, including analytical approximation, series solution techniques, integral equation approaches and numerical methods. Part 3 considers calibration problems of the Heston model, the Stein-Stein model and the local regime-Switching model with real market data.