Analysis Of Lookback Option In CEV Modified Model

In this paper we consider three problems in the lookback option pricing:At first, we assume the underlying asset follows the Constant Elasticity of Variance Diffusion, in the case of the existence of the transform costs in the market, we obtain a new model considering the transform costs in the lookback option pricing using the arbitrage theorem in the option pricing.At the same time, we get a numerical solution to the new model, give an analysis on its convergence and the consistence and prove the effective of the solution.At the second, because of the problem in the assume that the interest in the market is consistent, so we assume the interest in the market is stochastic in the form of C-I-R and get another new pricing lookback option model in the arbitrage theorem.we give one example about the new model, discuss the impact of the stochastic interest to the lookback option and the impact of the stochastic volatility to the pricing of option.At the last, the jump-diffusion model can explain the unexpected jump because of the political and economical event in the market. This paper derives a new lookback option pricing model using the assumption that the underlying asset follows the CEV jump-diffusion model which contains the two models'advantage above. This model captures the volatility smile and the unexpected jump because of the political and economical event and gives the improvement in the fixed volatility.