Research On Monte Carlo Simulation Method Pricing For American Basket Options

A basket option is an option on portfolio of several underlying assets, it is often much cheaper than an option on a single asset, which is the reason that a basket option is much more effective in the cost than a basket single asset option, With growing diversification in investor's portfolio, options on such portfolios are increasingly demanded.When dimension is higher, it is relatively cheaper to use Monte Carlo simulation since its computational cost does not increase exponentially as other methods. The ease exists only for European-style options. It is however known that the most difficult problems of pricing and hedging multi-asset basket options are those with both high dimensionality, for which we would like to use Monte Carlo simulation, and with early exercise, for which we would like to use either binomial tree or finite difference methods.This paper tries to apply the properties of a finite difference scheme can resolve early exercise problem to traditional Monte Carlo simulation method, so that solve the problem of pricing high dimensional derivatives(American basket options) with early exercise. The following is its basic process: First of all we use a finite difference scheme to analyse optimal exercise boundary. Basing on this result, we propose the boundary that depends on only one free parameter. The optimal parametric exercise boundary is searched via maximizing the expected discounted payoffs from simulated paths subject to variation of the free parameter. The expected discounted payoff corresponding to the optimal parametric exercise boundary is the final result for the American basket option price. In this paper, we use Monte Carlo simulation method and binomial tree to price American basket option on two underlying assets, we come to the following conclusions:(1) As the option price that is computed by these two numerical analytical methods is very near, which shows that we also can effectively price American option with early exercise by Monte Carlo simulation method.(2) For multi-asset high dimesional derivatives pricing problem, Monte Carlo simulation is a sort of very effective numerical analytical method, and its estimatestandard error and convergence does not depend on the dimension of the resolved problem, so it can be better used multi-asset high dimensional derivatives pricing problem.(3) When we use Monte Carlo simulation method to price American option, if it is combined with other methods, Monte Carlo will show greater advantage than binomial tree and finite difference.