含时间参数的离散障碍期权偏微分布朗模型的Romberg解法

Romberg numerical method for partial differential Brownian model with time parameter for discrete barrier option

为提高down-and-out离散障碍期权定价问题的求解精度,降低计算复杂度,本文提出一种具有离散时间参数的障碍期权偏微分布朗模型的Romberg求解方法.首先,本文将down-and-out离散障碍期权问题建模为带有时间参数的几何Brownian运动模型,该模型采用与时间无关的对应时间变换进行偏微分方程的期权定价;然后将得到的时间独立的偏微分方程转化为简单的热传导方程的积分形式,并给出了离散障碍期权定价定理;最后,采用Romberg求解方法,本文对离散障碍期权Brownian模型进行了求解.数值试验结果验证了方法的有效性.

In order to improve the numerical precision of down-and-out discrete barrier option pricing problem and reduce the computational complexity, we present a Romberg method for solving partial dif- ferential Brownian model with discrete time parameter. Firstly, the down-and-out discrete barrier option is modeled by a geometric Brownian motion model with time varying parameters, which uses time inde- pendent transformation to make option pricing with partial differential equation. Then, the time inde- pendent partial differential equation is transformed into a simple form of heat conduction equation. Fi- nally, the Romberg numerical method is used to solve the discrete barrier option Brownian model. An example is proposed to verify the effectiveness of the method.