Underlying Asset With Jumps European Option Pricing And Hedging

The main purpose of this article is to solve European option pricing and hedging in a jump-diffusion model in financial mathematics. In the Black-Scholes models, the stock price is driven by the Brown motion. It抯a continuous function of time. But some important events can lead to brusque variations in price. To model this kind of phenomena, we have to introduce discontinuous stochastic process.Under the assumption that the stock price is driven by the simple jump-diffusion process, the risk free rate and volatility are functions of time, by changes of probability measure, under the probability P~*, we obtain pricing formula and hedging of option in incomplete markets models.Further more; the stock price is driven by the Levy process. The risk free rate and volatility are stochastic process, by change of probability measure, under the probability Q, we obtain pricing formula and hedging of European option.