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A stochastic volatility Libor model and its robust calibration

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  • Denis Belomestny
  • Stanley Matthew
  • John Schoenmakers

Abstract

In this paper we propose a Libor model with a high-dimensional specially structured system of driving CIR volatility processes. A stable calibration procedure which takes into account a given local correlation structure is presented. The calibration algorithm is FFT based, so fast and easy to implement.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2007-067.pdf
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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2007-067.

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Length: 26 pages
Date of creation: Dec 2007
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2007-067

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Keywords: Libor modelling; stochastic volatility; CIR processes; calibration;

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  1. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, American Finance Association, vol. 52(1), pages 409-30, March.
  2. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers, Massachusetts Institute of Technology (MIT), Sloan School of Management 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  3. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
  4. Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 6(6), pages 513-536.
  5. 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, Society for Financial Studies, vol. 6(2), pages 327-43.
  6. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 13(3), pages 383-410.
  7. Denis Belomestny & John Schoenmakers, 2006. "A jump-diffusion Libor model and its robust calibration," SFB 649 Discussion Papers SFB649DP2006-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, Springer, vol. 11(1), pages 29-50, January.
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