具有时间参数离散障碍期权偏微分布朗模型的Romberg求解

为提高Down-and-Out离散障碍期权定价问题精度，降低计算复杂度，提出一种具有离散时间参数障碍期权偏微分布朗模型的Romberg求解方法。首先，将Down-and-Out离散障碍期权问题建模为随时间变化参数的几何Brownian运动模型，采用与时间无关的对应时间变换进行偏微分方程(PDE)的期权定价。然后，得到的时间独立的偏微分方程转化为简单的热传导方程积分形式，实现模型简化，并给出离散障碍期权定价定理；最后，采用Romberg求解过程实现了离散障碍期权Brownian模型的精确求解。实验结果验证了所提方法的有效性。

Romberg solution of partial differential Brown model with time parameter discrete barrier option

In order to improve the precision of Down-and-Out discrete barrier option pricing problem and reduce the computational complexity, this paper presented a Romberg method for solving partial differential Brown model with discrete time parameters. Firstly, we modeled the Down-and-Out discrete barrier option as the geometric Brownian motion model with time varying parameters, for partial differential equations used the corresponding time transform and time independent (PDE) option pricing. Then, the time independent partial differential equation is transformed into a simple form of heat conduction equation, and the model is simplified; Finally, the Romberg model is used to solve the discrete barrier option Brownian model. The experimental results verify the effectiveness of the proposed method.