Binomial Option Pricing Models with Monotonic and Smooth Convergence Property

Abstract

The recent literature indicates that the most efficient binomial models generally yield binomial option prices with monotonic and smooth convergence because one can apply the extrapolation formula to enhance the accuracy. In this paper, we first compare the pricing efficiency of four binomial models with monotonic and smooth convergence. These models include the binomial Black-Scholes (BBS) model of Broadie and Detemple (1996), the flexible binomial model (FB) of Tian (1999), the smoothed payoff (SPF) approach of Heston and Zhou (2000), and the generalized Cox-Ross-Rubinstein (GCRR) model of Chung and Shih (2007). Although these models have been proved to be efficient methods for pricing options, their efficiency for the calculation of delta and gamma is not known. To fill the gap of the literature, we then investigate the efficiency of these binomial models for calculating delta and gamma. The numerical results indicate that these models can also generate monotonic and smooth convergence estimates for deltas and gammas. Moreover, the GCRR-XPC model is the most efficient method to compute prices, deltas, and gammas for options.