ACHIEVING HIGHER ORDER CONVERGENCE FOR THE PRICES OF EUROPEAN OPTIONS IN BINOMIAL TREES
提出了一类新的二叉树来逼近Black-Scholes模型，证明了欧式期权价格存在完整渐近展开并显式计算前三项，构造了三阶收敛的树并证明了Leisen-Reimer树的二阶收敛猜想。
A new family of binomial trees as approximations to the Black–Scholes model is introduced. For this class of trees, the existence of complete asymptotic expansions for the prices of vanilla European options is demonstrated and the first three terms are explicitly computed. As special cases, a tree with third-order convergence is constructed and the conjecture of Leisen and Reimer that their tree has second-order convergence is proven.