A More Accurate Finite Difference Approximation for the Valuation of Options
提出一种比Schwartz近似更精确的有限差分方法，用于期权定价，并通过无股息股票看涨期权的例子验证其精度，同时指出该方法能消除Brennan和Schwartz发现的方差偏差。
option when a closed-form solution of the valuation equation cannot be ob? tained. This model is based on a difference approximation of the valuation equation and uses standard numerical methods. We intend to show here that the same methods can be used to derive a difference approximation of the solution of the valuation equation which has a greater level of accuracy than Schwartz's approximation. In the first section, we will show why the difference approximation that we will use is more accurate. We will also illustrate this greater level of accuracy by applying both the new difference approximation and Schwartz's algorithm to the valuation of a call option on a nondividend paying stock and by comparing the results obtained to the closed-form solution of Black and Scholes [1]. Finally, in Section ll,we will show that the algorithm proposed in Sec? tion I suppresses the bias that Brennan and Schwartz [2] found in the variance of the generalized jump process which approximates the diffusion process followed by the logarithm of the stock price. Conclusions also will be presented in this section.