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

Abstract:

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.