Efficient Willow Tree Method for Asian Option Pricing Under Merton JumpDiffusion Model

Abstract:

The logarithm of the stock price is described as a combination of a Brownian motion and a compound Poisson process in the jump diffusion model proposed by Merton, which can capture the negative skewness and high kurtosis of stock returns observed from the financial market. However, existing methods for the Asian option pricing under the jump diffusion model is quite expensive. Thus, an efficient and accurate willow tree method is proposed in this paper and its theoretical convergence is analyzed. Besides, some numerical experiments are conducted to demonstrate the efficiency and accuracy of the proposed method.

Key words:Asian option; jumpdiffusion model; willow tree method; Monte Carlo method