An iterative splitting method for pricing European options under the Heston model☆

Highlights：

• We focus on the Heston model and construct artificial boundary conditions (ABCs) for the problem in addition to the boundary condition in Heston’s original paper.

• Numerical experiments show that the iterative splitting method gives significantly better solutions compared to the classic 2-dimensional finite difference scheme no matter which ABC is chosen.

• The iterative splitting method has a big advantage as well when calculating the Greeks including Delta, Gamma and Vega which have received much attention in practice.

• Our new method transforms a 2-dimenstional problem into quasi 1-dimensional ones so that it helps to reduce computational cost and can be easily extended to other models for option valuation.

摘要

•In this paper, we propose an iterative splitting method as a combination of operator splitting and iterative methods to solve option pricing problems. To guarantee convergence, we use a mixed method to improve the numerical scheme. And a sufficient condition of the convergence of the iteration is given.•We focus on the Heston model and construct artificial boundary conditions (ABCs) for the problem in addition to the boundary condition in Heston’s original paper.•Numerical experiments show that the iterative splitting method gives significantly better solutions compared to the classic 2-dimensional finite difference scheme no matter which ABC is chosen.•The iterative splitting method has a big advantage as well when calculating the Greeks including Delta, Gamma and Vega which have received much attention in practice.•Our new method transforms a 2-dimenstional problem into quasi 1-dimensional ones so that it helps to reduce computational cost and can be easily extended to other models for option valuation.