  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).
