Artificial boundary method for the solution of pricing European options under the Heston model

TL;DR

This paper introduces an artificial boundary method with novel boundary conditions for efficiently and accurately pricing European options under the Heston model, improving upon traditional boundary approaches.

Contribution

The paper develops an asymptotic solution and artificial boundary conditions for the Heston model, enhancing numerical accuracy in option pricing.

Findings

Artificial boundary conditions improve pricing accuracy

Method outperforms traditional boundary conditions

Numerical experiments validate effectiveness

Abstract

This paper considers the valuation of a European call option under the Heston stochastic volatility model. We present the asymptotic solution to the option pricing problem in powers of the volatility of variance. Then we introduce the artificial boundary method for solving the problem on a truncated domain, and derive several artificial boundary conditions (ABCs) on the artificial boundary of the bounded computational domain. A typical finite difference scheme and quadrature rule are used for the numerical solution of the reduced problem. Numerical experiments show that the proposed ABCs are able to improve the accuracy of the results and have a significant advantage over the widely-used boundary conditions by Heston in the original paper (Heston, 1993).