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American option pricing under the double Heston model based on asymptotic expansion

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  • S. M. Zhang
  • Y. Feng

Abstract

This paper focuses on pricing American put options under the double Heston model proposed by Christoffersen et al. By introducing an explicit exercise rule, we obtain the asymptotic expansion of the solution to the partial differential equation for pricing American put options. We calculate American option price by the sum of the European option price and the early exercise premium. The early exercise premium is calculated by the difference between the American and European option prices based on asymptotic expansions. The European option price is obtained by the efficient COS method. Based on the obtained American option price, the double Heston model is calibrated by minimizing the distance between model and market prices, which yields an optimization problem that is solved by a differential evolution algorithm combined with the Matlab function fmincon.m. Numerical results show that the pricing approach is fast and accurate. Empirical results show that the double Heston model has better performance in pricing short-maturity American put options and capturing the volatility term structure of American put options than the Heston model.

Suggested Citation

  • S. M. Zhang & Y. Feng, 2019. "American option pricing under the double Heston model based on asymptotic expansion," Quantitative Finance, Taylor & Francis Journals, vol. 19(2), pages 211-226, February.
    • Handle: RePEc:taf:quantf:v:19:y:2019:i:2:p:211-226
    DOI: 10.1080/14697688.2018.1478119
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    Cited by:

    1. Youngin Yoon & Jeong-Hoon Kim, 2023. "A Closed Form Solution for Pricing Variance Swaps Under the Rescaled Double Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 429-450, January.
    2. Allan Jonathan da Silva & Jack Baczynski & José Valentim Machado Vicente, 2020. "Efficient Solutions for Pricing and Hedging Interest Rate Asian Options," Working Papers Series 513, Central Bank of Brazil, Research Department.
    3. Zhang, Sumei & Gao, Xiong, 2019. "An asymptotic expansion method for geometric Asian options pricing under the double Heston model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 1-9.

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