An integral equation representation approach for valuing Russian options with a finite time horizon

作者：Jeon Junkee; Han Heejae; Kim Hyeonuk; Kang Myungjoo^*

来源：Communications in Nonlinear Science & Numerical Simulation, 2016, 36: 496-516.

DOI：10.1016/j.cnsns.2015.12.019

• Russian option
• Free boundaty problem
• Integral equation
• Mixed boundary condition
• Recursive integration method
• Mellin transform

In this paper, we first describe a general solution for the inhomogeneous Black-Scholes partial differential equation with mixed boundary conditions using Mellin transform techniques. Since Russian options with a finite time horizon are usually formulated into the inhomogeneous free-boundary Black-Scholes partial differential equation with a mixed boundary condition, we apply our method to Russian options and derive an integral equation satisfied by Russian options with a finite time horizon. Furthermore, we present some numerical solutions and plots of the integral equation using recursive integration methods and demonstrate the computational accuracy and efficiency of our method compared to other competing approaches.

• 出版日期2016-7