最小叉熵方法推导期权定价二叉树模型

发布时间：2018-04-04 12:01

本文选题：期权定价　切入点：最小叉熵方法　出处：《大连理工大学学报》2011年05期

【摘要】：借助最小叉熵方法建立了新模型,即把标的资产(股票)价格看成一个信息系统,根据以往股票价格的历史信息给出股票价格的一个概率密度作为先验概率密度,然后在当前股票价格变化的随机变量的矩约束下,用最小叉熵方法来预测nΔt时间点末的股票价格分布最靠近先验概率的概率密度,从而得到参数p、u、d.新模型直接可用现有非线性规划算法进行求解或者转化为其对偶形式用无约束优化来求解,计算方便,经济、物理含义明确,有效克服了二叉树及其演化方法的不足,且不受股票价格变化运动形式限制,是一个统一的模型.与B-S、CRR、JR、TGR、Wil1、Wil2方法数值比较结果表明,多数情况下新方法收敛速度快,计算稳定.
[Abstract]:A new model is established by using the minimum cross-entropy method, that is, the underlying asset (stock) price is regarded as an information system, and a probability density of the stock price is given as a priori probability density according to the historical information of the stock price.Then under the moment constraint of the stochastic variable of the current stock price change, the probability density of the stock price distribution closest to the priori probability at the end of n 螖 t time point is predicted by using the minimum cross entropy method, and the parameter pu UD is obtained.The new model can be solved directly by existing nonlinear programming algorithms or transformed into its dual form. It is easy to calculate, economical and has clear physical meaning. It overcomes the deficiency of binary tree and its evolution method.And not limited by the movement of stock prices, is a unified model.The numerical results of the new method are compared with that of the B-S CRRN JRG TGRT Wil1W Wil2 method. The results show that the new method has a fast convergence rate and a stable calculation in most cases.
【作者单位】：大连理工大学数学科学学院;大连理工大学工业装备结构分析国家重点实验室;
【基金】：国家自然科学基金资助项目(重大项目10590354;10572031)
【分类号】：F830.91;F224

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