Asymptotic expansion method for pricing and hedging American options with two-factor stochastic volatilities and stochastic interest rate

ABSTRACT

We consider the pricing and hedging of American put options under the double Heston model with CIR stochastic interest rate. With an explicit exercise rule American option is approximated by barrier option for which the solution to the partial differential equation is derived by a short-maturity asymptotic expansion. Combining with control variate technique by Fourier-cosine expansion we analytically derive American puts prices and hedging parameters. We also construct a Delta-Vega-Rho hedging strategy of the proposed model for American puts and implement it by Monte Carlo simulation. Numerical results show that the presented pricing method is fast and accurate, the hedging performance of the proposed model is better than that of the BS, Heston and double Heston model.

KEYWORDS:

• American options
• option pricing
• hedging
• asymptotic expansion
• double Heston model
• stochastic interest rate

2010 AMS SUBJECT CLASSIFICATIONS:

• 91B70
• 91G20
• 91G60
• 65D20
• 60E10

Acknowledgements

The authors are grateful to Prof. Nikolai Dokuchaev for valuable suggestions that have substantially improved the paper. The authors are also grateful to Curtin university in Australia for laboratory and hardware equipment.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China under grant number [11601420], the Natural Science Foundation of Shaanxi Province, China under grant number [2017JM1021] and the Scientific Research Foundation of the Education Department of Shaanxi Province, China under grant number [17JK0714].