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 [26], 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 [17].

中文翻译：

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具有随机波动率和置换扩散的Libor市场模型的快速校准

本文展示了使用Edgeworth和Gram-Charlier扩展在校准具有随机波动率和位移扩散的Libor市场模型（DD-SV-LMM）中的效率。我们的方法汇集了两个研究领域；首先，自[26]，尤其是在矩生成函数上，其次是基于Edgeworth或Gram-Charlier展开的密度分布的近似值。通过探索直到四阶的矩的分析可延展性，我们能够对具有正常波动率的偏度和峰度的参考巴切里尔模型进行调整，并作为副产品得出将波动率与货币性相关的微笑公式。可解释的参数。作为主要结论，我们的数值结果表明，与[[]开发的经典数值积分方法相比，DD-SV-LMM校准过程的计算时间减少了98％。17]。