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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 On the Rate of Convergence of Binomial Greeks 563Journal of Futures Markets DOI: 10.1002/fut 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.

Using daily and intraday data, we investigate the cross‐sectional relation between stock prices and institutional trading in the Taiwan stock market. Consistent with the investigative herding hypothesis, we find that institutional herding exists because of institutional positive feedback trading behavior rather than following trades made by other institutions, as suggested by the information cascade hypothesis. Moreover, the positive correlation between institutional trade imbalance and stock returns mainly comes from institutional positive feedback trading. The institutional trading decisions rely on returns measured not only over the lagged trading day but also over the opening session during the same day.

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