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Multiscale Stochastic Volatility Model For Derivatives On Futures

Author

Listed:
  • JEAN-PIERRE FOUQUE

    (Department of Statistics and Applied Probability, University of California, Santa Barbara, 552 University Road, Santa Barbara, California 93106-3110, USA)

  • YURI F. SAPORITO

    (Department of Statistics and Applied Probability, University of California, Santa Barbara, 552 University Road, Santa Barbara, California 93106-3110, USA)

  • JORGE P. ZUBELLI

    (IMPA (Instituto de Matemática Pura e Aplicada), Estrada Dona Castorina 110, Rio de Janeiro, Rio de Janeiro 22460-320, Brazil)

Abstract

In this paper, we present a new method for computing the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility studied in Fouque et al. (2011). It provides an alternative method to the singular perturbation technique presented in Hikspoors & Jaimungal (2008). The main features of our method are twofold: firstly, it does not rely on any additional hypothesis on the regularity of the payoff function, and secondly, it allows an effective and straightforward calibration procedure of the group market parameters to implied volatilities. These features were not achieved in previous works. Moreover, the central argument of our method could be applied to interest rate derivatives and compound derivatives. The only pre-requisite of our approach is the first-order approximation of the underlying derivative. Furthermore, the model proposed here is well-suited for commodities since it incorporates mean reversion of the spot price and multiscale stochastic volatility. Indeed, the model was validated by calibrating the group market parameters to options on crude-oil futures, and it displays a very good fit of the implied volatility.

Suggested Citation

  • Jean-Pierre Fouque & Yuri F. Saporito & Jorge P. Zubelli, 2014. "Multiscale Stochastic Volatility Model For Derivatives On Futures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-31.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:07:n:s0219024914500435
    DOI: 10.1142/S0219024914500435
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
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    Cited by:

    1. Jean-Pierre Fouque & Sebastian Jaimungal & Yuri F. Saporito, 2021. "Optimal Trading with Signals and Stochastic Price Impact," Papers 2101.10053, arXiv.org, revised Aug 2023.
    2. Andrea Barletta & Elisa Nicolato & Stefano Pagliarani, 2019. "The short‐time behavior of VIX‐implied volatilities in a multifactor stochastic volatility framework," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 928-966, July.
    3. J.-P. Fouque & Y. F. Saporito, 2018. "Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 1003-1016, June.
    4. Min-Ku LEE & Sung-Jin YANG, PhD & Jeong-Hoon KIM, 2017. "Pricing Vulnerable Options with Constant Elasticity of Variance versus Stochastic Elasticity of Variance," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(1), pages 233-247.
    5. Łukasz Delong, 2019. "Optimal investment for insurance company with exponential utility and wealth-dependent risk aversion coefficient," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 73-113, February.

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