英文标题：
《Fast calibration of the Libor Market Model with Stochastic Volatility
and Displaced Diffusion》
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作者：
Laurent Devineau, Pierre-Edouard Arrouy, Paul Bonnefoy, Alexandre
Boumezoued
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最新提交年份：
2017
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英文摘要：
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).
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中文摘要：
本文证明了使用Edgeworth和Gram-Charlier展开式校准具有随机波动和位移扩散的Libor市场模型（DD-SV-LMM）的有效性。我们的方法将两个研究领域结合在一起；首先是自Wu和Zhang（2006）工作以来关于SV-LMM的结果，尤其是关于矩母函数的结果，其次是基于Edgeworth或Gram Charlier展开的密度分布近似。通过探索高达四阶矩的分析可处理性，我们能够使用偏态和峰度的正常波动率对参考Bachelier模型进行调整，并作为副产品，推导出波动率与货币性之间的微笑公式，以及可解释的参数。作为一个主要结论，我们的数值结果表明，与Heston（1993）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%。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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