跳扩散模型下亚式期权定价的柳树法研究

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

摘要:

Merton提出的对数跳扩散模型，将股票价格对数构造为布朗运动与复合泊松过程的叠加，能够更好地刻画股票价格回报的负偏度和过高峰度.由于现有的定价亚式期权的数值算法计算复杂、工作量大，因此提出了在Merton跳扩散模型下，亚式期权的快速定价柳树法,并从理论上证明了该算法的收敛性.通过数值实验，表明柳树法与现有方法相比有相同的计算精度，但计算速度更快.

关键词:亚式期权; 跳扩散模型; 柳树法; 蒙特卡洛方法

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