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On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

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  • Leitao, Álvaro
  • Grzelak, Lech A.
  • Oosterlee, Cornelis W.

Abstract

In this work, we propose a one time-step Monte Carlo method for the SABR model. We base our approach on an accurate approximation of the cumulative distribution function of the time-integrated variance (conditional on the SABR volatility), using Fourier techniques and a copula. Resulting is a fast simulation algorithm which can be employed to price European options under the SABR dynamics. Our approach can thus be seen as an alternative to Hagan’s analytic formula for short maturities that may be employed for model calibration purposes.

Suggested Citation

  • Leitao, Álvaro & Grzelak, Lech A. & Oosterlee, Cornelis W., 2017. "On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 461-479.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:461-479
    DOI: 10.1016/j.amc.2016.08.030
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    References listed on IDEAS

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    1. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    2. Bin Chen & Cornelis W. Oosterlee & Hans Van Der Weide, 2012. "A Low-Bias Simulation Scheme For The Sabr Stochastic Volatility Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-37.
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    6. U. Cherubini & E. Luciano, 2002. "Bivariate option pricing with copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 69-85.
    7. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
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    Cited by:

    1. Kirkby, J. Lars & Nguyen, Dang H. & Nguyen, Duy, 2020. "A general continuous time Markov chain approximation for multi-asset option pricing with systems of correlated diffusions," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. Julio Guerrero & Giuseppe Orlando, 2022. "Stochastic Local Volatility models and the Wei-Norman factorization method," Papers 2201.11241, arXiv.org.
    3. Leitao, Álvaro & Oosterlee, Cornelis W. & Ortiz-Gracia, Luis & Bohte, Sander M., 2018. "On the data-driven COS method," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 68-84.
    4. Shuaiqiang Liu & Lech A. Grzelak & Cornelis W. Oosterlee, 2022. "The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations," Risks, MDPI, vol. 10(3), pages 1-27, February.

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