A quick operator splitting method for option pricing

Abstract

This paper proposes a new efficient operator splitting method for option pricing problem under the Heston model, which is very popular in financial engineering. The key idea of this method is relying on eliminating the cross derivative term in partial differential equation in two dimension by some variable transformation techniques, and then decomposes the original equation in two dimensions into two partial differential equations in one dimension, which can be numerically solved efficiently. Moreover, this method not only keeps the differentiability of model parameters, but also preserves the positivity, monotonicity and convexity of the option prices. Numerical results for a European put option show that this method achieves accuracy of second-order in space and first-order in time, which are coinciding with the theoretical analysis results. Since the algorithm of this paper can be parallelized easily, the option pricing problems in high-dimension can also be dealt with, such as the Basket option written on several assets and etc. Our method can also be applied to pricing American options, Asian options and option pricing problems in stochastic interest-rate models.