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

Laurent Devineau (), Pierre-Edouard Arrouy (), Paul Bonnefoy () and Alexandre Boumezoued ()
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Laurent Devineau: R&D, Milliman, Paris - Milliman France
Pierre-Edouard Arrouy: R&D, Milliman, Paris - Milliman France
Paul Bonnefoy: R&D, Milliman, Paris - Milliman France
Alexandre Boumezoued: R&D, Milliman, Paris - Milliman France

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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).

Keywords: Libor Market Model; Stochastic Volatility; Displaced Diffusion; Swaption pricing; Model calibration; Edgeworth expansions; Gram-Charlier expansions (search for similar items in EconPapers)
Date: 2017-05-11
Note: View the original document on HAL open archive server: https://hal.science/hal-01521491v2
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Citations: View citations in EconPapers (2)

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