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LIBOR additive model calibration to swaptions markets

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  • Colino, Jesús P.
  • Nogales, Francisco J.
  • Stute, Winfried

Abstract

In the current paper, we introduce a new calibration methodology for the LIBOR market model driven by LIBOR additive processes based in an inverse problem. This problem can be splitted in the calibration of the continuous and discontinuous part, linking each part of the problem with at-the-money and in/out -of -the-money swaption volatilies. The continuous part is based on a semidefinite programming (convex) problem, with constraints in terms of variability or robustness, and the calibration of the Lévy measure is proposed to calibrate inverting the Fourier Transform.

Suggested Citation

  • Colino, Jesús P. & Nogales, Francisco J. & Stute, Winfried, 2008. "LIBOR additive model calibration to swaptions markets," DES - Working Papers. Statistics and Econometrics. WS ws085619, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws085619
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    References listed on IDEAS

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    1. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    2. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    3. A. D'Aspremont, 2003. "Interest rate model calibration using semidefinite Programming," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(3), pages 183-213.
    4. Brigo, Damiano & Mercurio, Fabio & Morini, Massimo, 2005. "The LIBOR model dynamics: Approximations, calibration and diagnostics," European Journal of Operational Research, Elsevier, vol. 163(1), pages 30-51, May.
    5. Colino, Jesús P., 2008. "Weak convergence in credit risk," DES - Working Papers. Statistics and Econometrics. WS ws085518, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Marco Avellaneda & Antonio ParAS, 1996. "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(1), pages 21-52.
    7. Michael Magill & Martine Quinzii (ed.), 2008. "Incomplete Markets," Books, Edward Elgar Publishing, volume 0, number 4204.
    8. repec:dau:papers:123456789/1392 is not listed on IDEAS
    9. Peter Carr & Hélyette Geman & Dilip Madan & Marc Yor, 2005. "Pricing options on realized variance," Finance and Stochastics, Springer, vol. 9(4), pages 453-475, October.
    10. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
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