非线性投资组合的风险会计：一种新的傅立叶方法
Accounting for risk of non linear portfolios: a novel Fourier approach
摘要：
非线性工具的存在是导致现实投资组合价格变化分布出现非高斯特征的原因，即使是正态分布的风险因素。对于基准Delta Gamma Normal模型尤其如此，该模型通常表现出指数衰减的幂律尾部。我们展示了如何知识的模型特征函数导致傅立叶表示的两个标准的风险措施，风险价值和预期损失，以及他们的敏感性相对于模型参数。我们详细的数值实现我们的公式，我们强调的可靠性和效率，我们的结果相比，蒙特卡罗模拟。
英文摘要：
The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power law tails. We show how the knowledge of the model characteristic function leads to Fourier representations for two standard risk measures, the Value at Risk and the Expected Shortfall, and for their sensitivities with respect to the model parameters. We detail the numerical implementation of our formulae and we emphasizes the reliability and efficiency of our results in comparison with Monte Carlo simulation.
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