Study Of Pricing Lookback Option In Fractional Stochastic Interest Rate Modeland Jump-diffusion Model

This paper mainly studies the problem of pricing European lookback option under the assumptions that the interest rate satisfies the fractional CIR model and the stock price obeys fractional jump-diffusion model.Applying partial differential method and equivalent quasi martingale measure method,in addition to stochastic analysis theory and the finite difference method,we have obtained respectively the price of the lookback option numerical solutions and analytical solutions.The results in this paper extend as well as improve previously known results.For partial differential method,the paper firstly uses the risk hedge technique and fractional Ito formula,an option pricing model and the differential equation of the model are derived.And the concrete numerical arithmetic scheme of the differential equation is obtained by using the finite difference method.Finally we verify the validity of the method by numerical experiments and discuss the effect of Poisson intensity? on the option prices.For equivalent quasi martingale measure method,the paper emphasizes the idea of measure transformation.Through fractional Girsanov theorem,the measure transformation under fractional Brown motion environment is carried out,by using the properties of conditional expectation,we get the explicit expressions for European lookback options prices and call-put parity.