最小叉熵方法推导期权定价二叉树模型  

Minimum cross entropy formalism of binomial tree model for option pricing

作　　者：李英华[1] 李兴斯[2] 

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024 [2]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024

出　　处：《大连理工大学学报》2011年第5期777-780,共4页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(重大项目10590354;10572031)

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n△t时闻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，有效克服了二又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．Using minimum cross entropy formalism, the new model was constructed, which takes the price states of the underlying asset （stock） as an information system. Firstly, the prior probability density from the historical data of the stock price was gained. Secondly, the probability density closest to the prior probability of the stock price distribution for the binomial tree model at the end of moment nat was derived by the minimum cross entropy formalism under the moments constraints of stock price change. Then, the parameters p, u, d were gained. The new model is not only easy in calculating because of being solved by the existing nonlinear programming algorithm or nonconstrained optimization through its dual problem, but also has clear economical and physical meaning. The new one tackles the drawbacks of the binomial model and its evolution, and is a unified model without being restricted by the type of the stock price probability distribution. Finally, compared with the B-S model, CRR model and JR model, TGR model, Wil1 model, Wil2 model, the calculation results show that the new method can more rapidly converge in most cases, and is more stable.

关 键 词：期权定价 最小叉熵方法 二叉树期权定价方法 

分 类 号：F830.9[经济管理—金融学]