Improved Hidden Markov ARMA-GARCH Model Forecasting In High Frequency Sample

Option pricing is always the hot topic in the area of financial mathematics. Since Black and Scholes introduced the B-S model, there have been a lot of studies on option pricing. Especially in recent years, the regime-switching model attracts much attention of scholars. As this model would 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 on regime-switching.In this paper, we fist give the stochastic differential equation of stock price under a regime-switching double exponential jump diffusion model. In this equation, the stock price volatility, the stock return rate and the jump intensity are all depend on the states of economy. Then, we apply the regime-switching Esscher transform to find an equivalent 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 double exponential distribution and option pricing: option pricing decreases with the increasing of1?, and increases while 2? increases, also with the increase of q, option pricing would decrease. Besides, we get that option pricing would increase with the adding of maturity data, and it would decrease when strike price increases.