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On the Approximation of the SABR with Mean Reversion Model: A Probabilistic Approach

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  • Joanne E. Kennedy
  • Duy Pham

Abstract

In this paper, we study the stochastic alpha beta rho with mean reversion model (SABR-MR). We first compare the SABR model with the SABR-MR model in terms of future volatility to point out the fundamental difference in the models' dynamics. We then derive an efficient probabilistic approximation for the SABR-MR model to price European options. Similar to the method derived in Kennedy, J. E., Mitra, S., & Pham, D. (2012). On the approximation of the SABR model: A probabilistic approach. Applied Mathematical Finance, 19 (6), 553-586., we focus on capturing the terminal distribution of the underlying asset (conditional on the terminal volatility) to arrive at the implied volatilities of the corresponding European options for all strikes and maturities. Our resulting method allows us to work with a wide range of parameters that cover the long-dated option and different market conditions.

Suggested Citation

  • Joanne E. Kennedy & Duy Pham, 2014. "On the Approximation of the SABR with Mean Reversion Model: A Probabilistic Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(5), pages 451-481, November.
    • Handle: RePEc:taf:apmtfi:v:21:y:2014:i:5:p:451-481
    DOI: 10.1080/1350486X.2014.888146
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    Cited by:

    1. Álvaro Leitao & Lech A. Grzelak & Cornelis W. Oosterlee, 2017. "On an efficient multiple time step Monte Carlo simulation of the SABR model," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1549-1565, October.

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