• Abstract

The quanto options pricing model is a typical two-dimensional Black-Scholes equation with a mixed derivative term, and it has been increasingly attracting interest over the last decade. A kind of improved alternating direction implicit methods, which is based on the Douglas-Rachford (D-R ADI) and Craig-Sneyd (C-S ADI) split forms, is given in this paper for solving the quanto options pricing model. The improved ADI methods first split the original problem into two separate one-dimensional problems, and then solve the tri-diagonal matrix equations at each time-step. There are several advantages in this method such as: parallel property, unconditional stability, convergency and better accuracy. The numerical experiments show that this kind of methods is very efficient compared to the existent explicit finite difference method. In addition, because of the natural parallel property of the improved ADI methods, the parallel computing is very easy, and about 50% computational cost can been saved. Thus the improved ADI methods can be used to solve the multi-asset option pricing problems effectively.

• Keywords

Quanto options pricing model two-dimensional Black-Scholes equation improved ADI method parallel computing numerical experiments

• AMS Subject Headings

65Y05 91B24

• Copyright

COPYRIGHT: © Global Science Press

• Email address