On the rate of convergence of binomial Greeks
研究了CRR模型及多种平滑价格收敛模型下二项式希腊字母（Delta和Gamma）的收敛模式与速度，证明收敛阶为O(1/n)，并发现将执行价置于树中心可显著提升精度，FB-XPC和GCRR-XPC模型结合两点外推法计算希腊字母效率最高。
Abstract This study investigates the convergence patterns and the rates of convergence of binomial Greeks for the CRR model and several smooth price convergence models in the literature, including the binomial Black–Scholes (BBS) model of Broadie M and Detemple J ( 1996 ), the flexible binomial model (FB) of Tian YS ( 1999 ), the smoothed payoff (SPF) approach of Heston S and Zhou G ( 2000 ), the GCRR‐XPC models of Chung SL and Shih PT ( 2007 ), the modified FB‐XPC model, and the modified GCRR‐FT model. We prove that the rate of convergence of the CRR model for computing deltas and gammas is of order O (1/ n ), with a quadratic error term relating to the position of the final nodes around the strike price. Moreover, most smooth price convergence models generate deltas and gammas with monotonic and smooth convergence with order O (1/ n ). Thus, one can apply an extrapolation formula to enhance their accuracy. The numerical results show that placing the strike price at the center of the tree seems to enhance the accuracy substantially. Among all the binomial models considered in this study, the FB‐XPC and the GCRR‐XPC model with a two‐point extrapolation are the most efficient methods to compute Greeks. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark