基于分数布朗运动和随机利率下两值期权定价  

Pricing Binary Option Based on Fractional Brownian Motion and Stochastic Interest Rate Model

作　　者：邓婷婷 韦才敏[1] DENG Tingting;WEI Caimin(Department of Mathematics, Shantou University, Shantou 515063, Guangdong, China)

机构地区：[1]汕头大学数学系,广东汕头515063

出　　处：《汕头大学学报（自然科学版）》2019年第1期29-38,共10页Journal of Shantou University：Natural Science Edition

基　　金：广东省自然科学基金项目(2017A030313005)

摘　　要：本文研究了标的资产服从分数布朗运动和利率服从Vasicek模型的两值期权定价问题.首先对零息票债券进行定价,得到零息票债券所满足的偏微分方程,并给出了满足此偏微分方程的仿射结构的解.其次,利用投资组合的Δ-对冲原理构造无风险资产,求得两值期权在分数布朗运动和Vasicek随机利率下所满足的偏微分方程.最后引入适当的组合变量,通过多次换元将两值期权的所满足的偏微分方程及其边界条件转化为热传导方程进行求解,进而得到两值期权定价公式.The problem of pricing of underlying asset obeying fractional Brownian motion when the interest rate is assumed to obey Vasicek stochastic interest rate is studied. Firstly, the price of zero coupon bond is set. The partial differential equation satisfied by zero coupon bond is obtained, and the solution of affine structure that satisfies this partial differential equation is obtained. Then, using the hedging principle of the portfolio to construct the riskless asset, the partial differential equation satisfied by binary option in the fractional Vasicek stochastic interest rate model is obtained. Finally, appropriate combination of variables is introduced. Through many times in yuan handling, binary option of partial differential equation and its boundary condition are transformed into heat conduction equation to solve binary option formula.

关 键 词：分数布朗运动 两值期权 随机利率 期权定价 

分 类 号：C935[经济管理—管理学] F224.3