Year

2017

Degree Name

Doctor of Philosophy

Department

School of Mathematics and Applied Statistics

Abstract

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.

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