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Fast calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion

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  • Laurent Devineau
  • Pierre-Edouard Arrouy
  • Paul Bonnefoy
  • Alexandre Boumezoued

Abstract

This paper demonstrates the efficiency of using Edgeworth and Gram-Charlier expansions in the calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion (DD-SV-LMM). Our approach brings together two research areas; first, the results regarding the SV-LMM since the work of Wu and Zhang (2006), especially on the moment generating function, and second the approximation of density distributions based on Edgeworth or Gram-Charlier expansions. By exploring the analytical tractability of moments up to fourth order, we are able to perform an adjustment of the reference Bachelier model with normal volatilities for skewness and kurtosis, and as a by-product to derive a smile formula relating the volatility to the moneyness with interpretable parameters. As a main conclusion, our numerical results show a 98% reduction in computational time for the DD-SV-LMM calibration process compared to the classical numerical integration method developed by Heston (1993).

Suggested Citation

  • Laurent Devineau & Pierre-Edouard Arrouy & Paul Bonnefoy & Alexandre Boumezoued, 2017. "Fast calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion," Papers 1706.00263, arXiv.org.
    • Handle: RePEc:arx:papers:1706.00263
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    Cited by:

    1. Pierre-Edouard Arrouy & Sophian Mehalla & Bernard Lapeyre & Alexandre Boumezoued, 2020. "Jacobi Stochastic Volatility factor for the Libor Market Model," Working Papers hal-02468583, HAL.
    2. Fabrice Borel-Mathurin & Nicole El Karoui & Stéphane Loisel & Julien Vedani, 2020. "Locality in time of the European insurance regulation "risk-neutral" valuation framework, a pre-and post-Covid analysis and further developments," Working Papers hal-02905181, HAL.

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