Pricing European Options Under Markov-modulated Jump-diffusion Models

There are31types of commodity futures and one type of stock index future are be-ing traded in derivative market of China. The list of option has progressively developedin the last two years.In2012,several exchanges, including the Zhengzhou Commodity Ex-change,highlight the innovation of option and activate the simulated trading of options.Manyprofessional experts say that the era of options is coming.The point of option trading is ac-curate pricing and valuation.This thesis investigates the pricing of option when the dynamics of the risky under-lying asset are governed by a markov-modulated jump diffusion model.We suppose that therisk free rate,the appreciation rate,the volatility and the jump intensity of the underlying riskyasset are depend on the state of the economy,whick is formulated by a continuous-time finite-state markov chain.Here we will adopt the esscher transform of Gerber and Shiu(1995) andThe First Fundamental Theorem of Asset Pricing to identify a risk-neutral martingale mea-sure in the incomplete market setting.Then we get an integral expression on the price ofEuropean call option on the risk-neutral martingale measure.Finally,numerical illustrationsare presented.