Efficient Discrete Time Jump Process Models in Option Pricing
通过高斯-埃尔米特求积法推导出一族跳跃过程模型，用于期权定价，并设计了一种“锐化”三叉树模型，在关键执行点处处理一阶导数不连续性，精度优于传统二叉树和三叉树模型。
A family of jump process models is derived by applying Gauss-Hermite quadrature to the recursive integration problem presented by a compound option model. The result is jump processes of any order with known efficiency properties in valuing options. In addition, these processes arise in the replication of options over finite periods of time with two or more assets where they again have known efficiency properties. A “sharpened” trinomial process is designed that accounts for the first-derivative discontinuity in option valuation functions at critical exercise points. It is shown to have accuracy superior to that of conventional binomial and trinomial processes and is nearly identical to the trinomial process optimized by Boyle (1988) through trial and error.