跳-分形过程下亚洲幂期权定价的一种高精度隐式差分格式及其稳定性和收敛性分析

A High-precision Implicit Difference Scheme for Asian Power Option Pricing Under Jump-fractal Process and Its Stability and Convergence Analysis

亚洲幂型期权路径复杂,通常情况下没有解析定价结果.本文在分数跳扩散模型下考察了亚洲幂型期权定价问题.针对该类型期权,得到了一个时间2阶、空间4阶精度的隐式差分格式.然后采用递推法,研究了隐式差分格式在无穷范数下的稳定性和收敛性.最后利用差分格式分析了亚洲幂型期权的数值模拟结果.

In general,there is no analytic pricing result for Asian power options.In this paper,we discuss the numerical simulation of this Asian power options under the fractional jump diffusion model.A discrete implicit numerical scheme with a spatially 4 order accuracy and a temporally 2 order accuracy is constructed.Then,the stability and convergence of the difference scheme with initial value is proved by using the recurrence method.Finally,we use the implicit numerical scheme and the above numerical technique to simulate the Asian power options.