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Fast swaption pricing under the market model with a square-root volatility process

Listed author(s):
  • Lixin Wu
  • Fan Zhang
Registered author(s):

    In this paper we study a correlation-based LIBOR market model with a square-root volatility process. This model captures downward volatility skews through taking negative correlations between forward rates and the multiplier. An approximate pricing formula is developed for swaptions, and the formula is implemented via fast Fourier transform. Numerical results on pricing accuracy are presented, which strongly support the approximations made in deriving the formula.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680701310961
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    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 8 (2008)
    Issue (Month): 2 ()
    Pages: 163-180

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    Handle: RePEc:taf:quantf:v:8:y:2008:i:2:p:163-180
    DOI: 10.1080/14697680701310961
    Contact details of provider: Web page: http://www.tandfonline.com/RQUF20

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    1. D. Brigo & F. Mercurio, 2003. "Analytical pricing of the smile in a forward LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 15-27.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    4. Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
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    6. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410.
    7. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    9. Alan Brace & Dariusz G¬łatarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
    10. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    11. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    12. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, September.
    13. Nicolas Merener & Paul Glasserman, 2003. "Numerical solution of jump-diffusion LIBOR market models," Finance and Stochastics, Springer, vol. 7(1), pages 1-27.
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