The Numerical Approximation Of Butterfly Option Price

Fouque and Ren give the approximation method of European derivatives prices under uncertain volatility model in the worst case scenario.To approximate the option prices,they use V0+ ?V1when V0 is the European derivatives price under Black-Scholes model and V1 satisfies a nonlinear partial differential equation.However,we can not get the analytical solution from the approximation method and they don't give the numerical method to solve the equation.In this paper,on the basis of this approximation method,we first use implicit difference method to give the iterative format of butterfly option price's numerical solution in the worst case scenario under uncertain volatility model and then we prove the stability of iterative format.There is a certain guiding significance for the simulation analysis of butterfly option price under uncertain volatility model.Next,we use the method of martingale to estimate the parameters of Hull-White stochastic volatility model.Then,we give the approximation of butterfly option price by Taylor expansion,and ultimately the option price estimation is given.Finally,as application,we simulate the price of these models.It can be seen from the simulation results that the prices of three models have the same changing trend.Among them,the prices under uncertain volatility model are always higher than those under Black-Scholes model,and the prices under stochastic volatility model go up and down in the prices of the others.In addition,in order to get further analysis of the relationship between ambiguity degrees and butterfly option price under uncertain volatility model,we simulate the same options which are in the different ambiguity degrees.Then we can get that the option prices increase with the rising of the model ambiguity degrees.