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

TL;DR

This paper introduces an iterative splitting method for efficiently solving the PDEs in European option pricing under the Heston model, improving accuracy and reducing computational costs.

Contribution

The paper presents a novel iterative splitting approach that transforms 2D PDEs into quasi 1D equations, enhancing computational efficiency and accuracy in option pricing.

Findings

The iterative splitting method outperforms classic finite difference methods in accuracy.

Using an artificial boundary condition improves the precision of option prices and Greeks.

The method effectively reduces computational costs for solving Heston model PDEs.

Abstract

In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation (PDE). We take the European option as an example and conduct numerical experiments using different boundary conditions. The iterative splitting method transforms the two-dimensional equation into two quasi one-dimensional equations with the variable on the other dimension fixed, which helps to lower the computational cost. Numerical results show that the iterative splitting method together with an artificial boundary condition (ABC) based on the method by Li and Huang (2019) gives the most accurate option price and Greeks compared to the classic finite difference method with the commonly-used boundary conditions in Heston (1993).