多元混合正态分布情形下的外汇期权组合非线性VaR模型

Nonlinear VaR model of FX options portfolio under multivariate mixture of normal distributions

提出了一种多元厚尾分布情形下的外汇期权组合非线性VaR模型.用多元混合正态分布来描述汇率回报分布厚尾特征,推导出多元混合正态分布情形下的反映外汇期权组合价值变化的矩母函数;在此基础上,利用特征函数和矩母函数关系,进一步将概率分布的Fourier-Inversion方法和数值积分近似计算的迭代算法——自适应Simpson法则发展到多元混合正态分布情形下的外汇期权组合非线性VaR模型中,估计出期权组合的VaR值.数值结果表明:使用Fourier-Inversion方法得到的VaR值与使用MonteCarlo模拟方法得到的VaR值相差不大,但使用Fourier-Inversion方法的计算速度明显快于Monte Carlo模拟方法.

The paper proposes a kind of nonlinear VaR model of FX options portfolio under heavy-tailed exchange rate returns.The paper depicts heavy-tailed exchange rate returns using multivariate mixture of normal distribution,and derives the moment generating function that reflects the change in FX option portfolio value.Moreover,to make use of the relationship between characteristic function and moment generating function,the paper develops Fourier-Inversion method and adaptive Simpson rule with iterative algorithm of numerical integration into non-linear VaR model of FX option portfolio,and calculates the VaR values of portfolio.Numerical results show that the VaR values using Fourier-Inversion method is slight difference in the VaR values using Monte Carlo simulation method.However,the calculation speed using Fourier-Inversion method is obviously quicker than the speed using Monte Carlo simulation method.