On Several Numerical Methods Of American Put Options

This article mainly studies the effective numerical methods of American put options.We start from the simplest structured method of American option pricing,and discuss the option pricing method based on the Black-Scholes equation.Then we reveal the relationship between the different methods.On the basis of comparing existing research methods,a least square Monte Carlo method with stochastic volatility is proposed.The basic idea of this method is to use fractional geometric Brownian motion to simulate the sample path of stochastic volatility,and then to calculate the price of American put options by combining with the least square method.Among them,we use a set of basis functions to describe the holding value function before the expiry time of American options with regression,and select the optimal stopping time by comparing the intrinsic value and holding value.Numerical experiment results show that the price of American options with stochastic volatility is higher than the price of American options under constant volatility.It is consistent with the high returns corresponding to the high risks in economics.