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American option valuation under time changed tempered stable Lévy processes

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  • Gong, Xiaoli
  • Zhuang, Xintian

Abstract

Given that the underlying assets in financial markets exhibit stylized facts such as leptokurtosis, asymmetry, clustering properties and heteroskedasticity effect, this paper presents a novel model for pricing American option under the assumptions that the stock price processes are governed by time changed tempered stable Lévy process. As this model is constructed by introducing random time changes into tempered stable (TS) processes which specially refer to normal tempered stable (NTS) distribution as well as classical tempered stable (CTS) distribution, it permits infinite jumps as well as capturing random varying time in stochastic volatility, consequently taking into account the empirical facts such as leptokurtosis, skewness and volatility clustering behaviors. We employ the Fourier-cosine technique to calculate American option and propose the improved Particle Swarm optimization (IPSO) intelligent algorithm for model calibration. To demonstrate the advantage of the constructed model, we carry out empirical research on American index option in financial markets across wide ranges of models, with the time changing normal tempered stable distribution model yielding a superior performance than others.

Suggested Citation

  • Gong, Xiaoli & Zhuang, Xintian, 2017. "American option valuation under time changed tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 57-68.
    • Handle: RePEc:eee:phsmap:v:466:y:2017:i:c:p:57-68
    DOI: 10.1016/j.physa.2016.09.005
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    Cited by:

    1. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
    2. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Gong, Xiaoli & Zhuang, Xintian, 2017. "Pricing foreign equity option under stochastic volatility tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 83-93.
    4. Jean-Philippe Aguilar & Cyril Coste & Jan Korbel, 2017. "Series representation of the pricing formula for the European option driven by space-time fractional diffusion," Papers 1712.04990, arXiv.org, revised Oct 2018.

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