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

On the Approximation of the SABR with Mean Reversion Model: A Probabilistic Approach AbstractIn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

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

Kennedy, Joanne E.; Pham, Duy
Applied Mathematical Finance , Volume 21 (5): 31 – Sep 3, 2014
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On the Approximation of the SABR with Mean Reversion Model: A Probabilistic Approach

Abstract

AbstractIn 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...
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Publisher
Taylor & Francis
Copyright
© 2014 Taylor & Francis
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2014.888146
Publisher site
See Article on Publisher Site

Abstract

AbstractIn 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.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Sep 3, 2014

Keywords: SABR; SABR-MR model; displaced diffusion; stochastic volatility; forward smile

References

  • Stochastic volatility corrections for interest rate derivatives
  • Mean-reverting stochastic volatility
  • Gaussian bridges
  • Managing smile risk
  • On the approximation of the SABR model: A probabilistic approach
  • Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model
  • Option pricing under stochastic volatility: The exponential Ornstein-Uhlenbeck model
  • Stochastic volatility model with time-dependent skew
  • A time-homogeneous, SABR consistent extension of the LMM
  • Linking caplets and swaption prices in the LMM-SABR model
  • Displaced discussion as an approximation of the constant elasticity of variance