An Efficient Tree Method in Option Pricing

We develop an efficient distribution-based tree method to value a broad range of contingent claims under Gaussian HJM framework of stochastic interest rates. Instead of using random numbers from the standard normal at each time interval of Monte Carlo simulation, we use a zero-mean and unit-variance bell-shaped multinomial distribution to approximate the standard normal distribution. Based on these multinomial distributions, we create a multinomial distribution-based tree to implement for at least ten-years maturity American-style contingent claims with arbitrary deterministic volatilities of interest rates under multi-factor Gaussian HJM framework. From the numerical results, the distribution-based tree method can be used to compute options prices fast with accuracy.