Heston随机波动模型时变利率下支付红利的timer期权定价  

The Timer Option Pricing with Paying Dividends Under the Time-Varying Interest Rates for Heston Stochastic Volatility Model

作　　者：王继霞[1] 王添秀 WANG Jixia;WANG Tianxiu(College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《应用数学》2018年第4期919-926,共8页Mathematica Applicata

基　　金：国家自然科学基金项目(U1504701);河南师范大学博士科研启动项目(qd15184);河南师范大学研究生创新基金(YL201703)

摘　　要：本文研究了在Heston随机波动模型下,连续支付红利的timer期权定价的条件Black-Scholes-Merton型公式.首先,利用投资组合的?-对冲原理构造无风险资产,给出了timer期权在Heston随机波动模型下所满足的偏微分方程.然后利用拉普拉斯逆变换得到了与贝塞尔过程相关的联合密度函数的显式公式.最后得到支付红利下timer期权定价的Black-Scholes-Merton型公式.This paper studies the conditional Black-Scholes-Merton formula for the time-varying interest rates of the timer option pricing with continuous paying dividends under Heston stochastic volatility model. The risk-free assets are constructed by using the ？-hedging principle of portfolio, and the partial differential equations are obtained which satisfies the timer option pricing under the Heston stochastic volatility model. The explicit formulas of the joint density function related to Bessel processes are obtained by using Laplace inverse transform and the Black-Scholes-Merton formula for the timer option pricing under the paying dividends is given.

关 键 词：timer期权定价 Heston随机波动模型 贝塞尔过程 时变利率 红利支付 

分 类 号：F830.9[经济管理—金融学] O211.1[理学—概率论与数理统计]