| Lookback option is a strong path-dependent option.Its strike price depends on the price of the underlying asset within the "lookback period".Because of the high return and the high price on the option,it has the vital significance to price the option more accurately.Based on the actual situation,the interest rate is a constant,the price of the underlying asset obeys geometric Brownian motion,and the fact that transaction costs are not considered has seriously affected the accuracy of option pricing.Therefore,this article studies the above situations.The main contents are as follows:(1)Under the Vasicek interest rate model,using the It?’s lemma and portfolio strategy,the pricing model of the European lookback put option is obtained when the price of the underlying asset obeys the standard Brownian motion and has a transaction costs.Then the differential equations are solved by using the unit conversion and variable substitution method,and the pricing formula of European lookback put options is obtained.(2)At first the partial differential equation model of the option pricing based on fractional Brownian motion was established by use of the It?’s lemma and the portfolio strategy.Then the model was simplified with unit conversion and variable substitution,the numerical solution was obtained through Crank-Nicolson scheme.Finally,numerical experiments were provided to confirm the effect of each pricing parameter.(3)Under the fractional Vasicek rate model,this part mainly studied the pricing problem of the European lookback option with the transaction cost of the underlying stock price obeying the fractional jump-diffusion process.By applying the no-arbitrage principle and the fractional It?’s formula,the partial differential equation was obtained.The pricing formula of European lookback put option was obtained by applying the unit conversion and variable substitution method to the differential equation.Finally,the validity of the method was verified by numerical experiments. |
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