跳跃-扩散模型中期权定价的倒向随机微分方程方法及等价概率鞅测度  

Option Pricing by the Backward Stochastic Differential Equation Method and the Equivalent Probability Martingale Measure in the Jump-diffusion Model

作　　者：范玉莲[1] 孙志宾[1] 

机构地区：[1]北方工业大学理学院,北京100144

出　　处：《应用数学学报》2009年第4期673-681,共9页Acta Mathematicae Applicatae Sinica

基　　金：北京市优秀人才培养(20081D0500200116);北京市专项"金融数学科研创新平台建设"(PXM2009014212;PXM2009077239);北京市教委计划(KM200910009009)资助项目

摘　　要：本文研究的是跳跃-扩散模型中的期权定价问题。通过研究该模型中未定权益所对应的倒向随机微分方程,找到市场中的一个等价概率鞅测度,借助测度变换,未定权益的定价问题就可转化为在等价概率鞅测度下的求期望问题。利用该方法,本文解得了标的股票价格过程为带非时齐Poisson跳跃的扩散过程且股价期望增长率,波动率,无风险利率均为时间函数时欧式期权价格公式。并且,借助倒向随机微分方程找到在以上参数均为常数时,期权价格所满足的偏微分方程。This paper studies the option pricing problem in the jump-diffusion model. By the backward stochastic differential equation method,we get the equivalent probability martingale measure.Then the option pricing problem can be converted to the expectation calculation problem under the equivalent probability martingale measure.We get the European option price formula when the underlying stock price process is nonhomogeneous Poisson jump-diffusion process with time-varying expected growth rate,volatility and risk.less rate. And by the backward stochastic differential equation we get the corresponding partial differential equation of the European option price when those parameters are con- stants.

关 键 词：期权定价 跳跃-扩散模型 等价概率鞅测度 倒向随机微分方程 

分 类 号：F224.7[经济管理—国民经济] O211.6[理学—概率论与数理统计]