摘要翻译：
我们在风险管理的背景下介绍了广义傅立叶变换的形式。我们开发了一个通用的框架来有效地计算最流行的风险度量，在险价值和预期缺口（也称为条件在险价值）。我们的方法所需要的唯一成分是描述使用中的金融数据的特征函数的知识。这使得风险分析可以扩展到那些定义在傅立叶空间中的非高斯模型，如Levy噪声驱动过程和随机波动率模型。我们在来自各种金融指数的数据集上检验了我们的分析结果，发现我们的预测优于标准对数正态动力学提供的预测，并与基准历史方法的预测显著一致。
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英文标题：
《A Generalized Fourier Transform Approach to Risk Measures》
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作者：
G. Bormetti, V. Cazzola, G. Livan, G. Montagna and O. Nicrosini
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最新提交年份：
2012
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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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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英文摘要：
  We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework to efficiently compute the most popular risk measures, Value-at-Risk and Expected Shortfall (also known as Conditional Value-at-Risk). The only ingredient required by our approach is the knowledge of the characteristic function describing the financial data in use. This allows to extend risk analysis to those non-Gaussian models defined in the Fourier space, such as Levy noise driven processes and stochastic volatility models. We test our analytical results on data sets coming from various financial indexes, finding that our predictions outperform those provided by the standard Log-Normal dynamics and are in remarkable agreement with those of the benchmark historical approach.
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PDF链接：
https://arxiv.org/pdf/0909.3978