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Stochastic volatility for interest rate derivatives

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  • Linus Kaisajuntti
  • Joanne Kennedy

Abstract

This paper uses an extensive set of market data of forward swap rates and swaptions covering 3 July 2002 to 21 May 2009 to identify a two-dimensional stochastic volatility process for the level of rates. The process is identified step by step by increasing the requirement of the model and introducing appropriate adjustments. The first part of the paper investigates the smile dynamics of forward swap rates at their setting dates. Comparing the SABR (with different ) and Heston stochastic volatility models informs us what different specifications of the driving SDEs have to offer in terms of reflecting the dynamics of the smile across dates. The outcome of the analysis is that a normal SABR model ( ) satisfactorily passes all tests and seems to provide a good match to the market. In contrast, we find that the Heston model does not. The next step is to seek a model of the forward swap rates (in their own swaption measure) based on only two Brownian motions that enables a specification with common parameters. It turns out that this can be done by extending the SABR model with a time-dependent volatility function and a mean-reverting volatility process. The performance of the extended (SABR with mean-reversion) model is analysed over several historical dates and is shown to be a stable and flexible choice that allows for good calibration across expiries and strikes. Finally, a time-homogeneous candidate stochastic volatility process that can be used as a driver for all swap rates is identified. This candidate process may in future work be used as a building block for a separable stochastic volatility LIBOR market model or a stochastic volatility Markov-functional model.

Suggested Citation

  • Linus Kaisajuntti & Joanne Kennedy, 2014. "Stochastic volatility for interest rate derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 457-480, March.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:3:p:457-480
    DOI: 10.1080/14697688.2012.757848
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    References listed on IDEAS

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    1. Anders B. Trolle & Eduardo S. Schwartz, 2010. "An Empirical Analysis of the Swaption Cube," NBER Working Papers 16549, National Bureau of Economic Research, Inc.
    2. Marc Henrard, 2004. "Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas," Finance 0407018, University Library of Munich, Germany, revised 27 Sep 2005.
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    Cited by:

    1. Emilio Russo & Alessandro Staino, 2018. "A Lattice-Based Model For Evaluating Bonds And Interest-Sensitive Claims Under Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-18, June.

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