European Option Pricing Under A Regime Switching Double Exponential Jump-diffusion Process

Option pricing is always the hot topic in the area of financial mathematics. Since Blackand Scholes introduced the B-S model, there have been a lot of studies of option pricing. Inrecent years, the regime switching model attracts much attention of scholars. As this modelwould describe both the status of financial market and varies of stock price more practically,it is significant to derive the option pricing formula on various specific models based onregime-switching.In this paper, we first give the stochastic differential equation of stock price under aregime-switching double exponential jump-diffusion model. In this equation, the stockprice volatility, the stock appreciation rate and the jump intensity are all depend on thestates of economy. Then, we apply the regime-switching Esscher transform to find anequivalent martingale measure and get the stochastic differential equation of stock price,also the pricing formula of European call option under the new measure is given. At last,we use Monte-Carlo simulation to get the relationship between each parameters of doubleexponential distribution and option pricing: option pricing decreases with the increasingof1, and increases while2increases, also with the increase of q, option pricing woulddecrease. Besides, we get that option pricing would increase with the adding of maturitydate, and it would decrease when strike price increases.