An analytical approximation method for pricing barrier options under the double Heston model

Abstract

The purpose of the paper is to provide an efficient pricing method for single barrier options under the double Heston model. By rewriting the model as a singular and regular perturbed BS model, the double Heston model can separately mimic a fast time-scale and a slow time-scale. With the singular and regular perturbation techniques, we analytically derive the first-order asymptotic expansion of the solution to a barrier option pricing partial differential equation. The convergence and efficiency of the approximate method is verified by Monte Carlo simulation. Numerical results show that the presented asymptotic pricing method is fast and accurate.

Keywords:

• Asymptotic expansion
• barrier option
• option pricing
• perturbation technique
• stochastic volatility

Additional information

Funding

This work is supported by the National Natural Science Foundation of China under Grant number 11601420, the China Scholarship Council (CSC) under Grant number 201708615097, the Natural Science Foundation of Shaanxi Province, China under Grant number 2017JM1021 and the Science Research Foundation of the Education Department of Shaanxi Province, China under Grant number 17JK0714. This work is also supported by Curtin university in Australia.