连续型向上敲出巴黎期权定价隐式差分格式及其稳定性和收敛性分析

Implicit Difference Scheme and Its Stability and Convergence Analysis for Continuous Up-and-Out Paris Option Pricing

考虑连续型向上敲出巴黎期权定价问题.首先,针对该类型巴黎期权,给出一个时间1阶、空间2阶精度的隐式差分格式;其次,采用不等式放大方法和Fourier展开方法分别讨论差分格式的稳定性、可解性和收敛性;最后,利用差分格式分析连续型向上敲出巴黎期权的数值定价结果.

We considered the continuous up-and-out Paris option pricing problem.Firstly,an implicit difference scheme with the first order in time and the second order in space was given for this type of Paris option.Secondly,the inequality amplification method and Fourier expansion method were used to discuss the stability,solvability and convergence of the difference scheme,respectively.Finally,the numerical pricing results of continuous up-and-out Paris options were analyzed by using the difference scheme.