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A closed-form option pricing approximation formula for a fractional Heston model

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Abstract

We present a method to develop simple option pricing approximation formulas for a fractional Heston model, where the volatility process is defined by means of a fractional integration of a diffusion process. This model preserves the short-time behaviour of the Heston model, at the same time it explains the slow decrease of the smile amplitude when time to maturity increases. Then, by means of classical Itô's calculus we decompose option prices as the sum of the classical Black-Scholes formula with volatility parameter equal to the root-mean-square future average volatility plus a term due to correlation and a term due to the volatility of the volatility. This decomposition procedure does not need the volatility process to be Markovian and allows us to develop easy-to-apply approximation formulas for option prices and implied volatilities, as well as to study their accuracy. Numerical examples are given.

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  • Elisa Alòs & Yan Yang, 2014. "A closed-form option pricing approximation formula for a fractional Heston model," Economics Working Papers 1446, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1446
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    Cited by:

    1. Hideharu Funahashi & Masaaki Kijima, 2017. "Does the Hurst index matter for option prices under fractional volatility?," Annals of Finance, Springer, vol. 13(1), pages 55-74, February.
    2. Christa Cuchiero & Josef Teichmann, 2019. "Markovian lifts of positive semidefinite affine Volterra type processes," Papers 1907.01917, arXiv.org, revised Sep 2019.
    3. Elisa Alòs & Jorge A. León, 2014. "On the second derivative of the at-the-money implied volatility in stochastic volatility models," Economics Working Papers 1458, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2016.
    4. Siow Woon Jeng & Adem Kilicman, 2020. "Series Expansion and Fourth-Order Global Padé Approximation for a Rough Heston Solution," Mathematics, MDPI, vol. 8(11), pages 1-26, November.
    5. Omid Jenabi & Nazar Dahmardeh Ghale No, 2018. "Option Pricing in Stochastic Volatility Models Driven by Fractional Jump-Diffusion Processes," International Journal of Finance, Insurance and Risk Management, International Journal of Finance, Insurance and Risk Management, vol. 8(1), pages 1374-1374.

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    More about this item

    Keywords

    Stochastic volatility; Heston model; Itô's calculus; fractional Brownian motion;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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