基于三叉树模型的美式期权定价及其Matlab算法

American Option Pricing Based on Trinomial Tree Model and Its Matlab Procedure

研究了存在连续红利的美式期权定价的数值解法,通过寻找三叉树模型中各个结点处标的资产价格的通项公式,得到了美式期权数值解的迭代公式及Matlab算法,结合Matlab比较了三叉树模型的稳定性优于二叉树模型,并通过控制变量法,直观地得到了美式期权价值对其各个影响因素的敏感性结果分析:美式看涨期权的价值与无风险利率、标的资产价格及其波动率和期权持有期呈正相关,与敲定价格呈负相关。

In this paper, we studied the numerical solution of American option pricing with continuous bonus. By looking for the general formula of asset price in each node of the Trinomial Tree method, we obtained the iterafive formula and Matlab procedure of numerical solution of American option. By comparison, we concluded the stability of the Trinomial Tree was better than that of the Binary Tree model. And the sensitivity of the American option value to each of its influencing factors was analyzed intuitively by means of the control variable method. The value of the American call option was positively correlated with the risk-free interest rate, the underlying asset price, the volatility and the holding period of the option, but negatively with the finalized price.