Correlation and Integration – from a destructive formula in finance
韓傳祥教授清華大學計量財務金融學系 下午 13:30–14:30 鴻經館 107 室Credit risk associated with credit derivatives has impacted our financial systems tremendously. The Gaussian copula plays a crucial role for the boost of credit derivative market because the correlation structure and its risk are easy to be built and calculated, respectively. Due to the simplicity of Gaussian copula, it has been blamed for the collapse of the trillion-dollar credit derivative market.
In this talk, I will start from a Gaussian integration but in high dimension. An efficient importance sampling method to measure dependence tail risk is justified asymptotically and its numerical performance is compared with mvncdf.m, a Matlab code. Then we generalize these results to (1) estimation of probabilities associated with order statistics and multivariate Student-t distribution, and (2) the first passage time problem related to stochastic systems. In the end, I shall introduce a nonparametric Fourier transform method and its correction schemes for estimation of the dynamic volatility matrix. This allows a new era for accessing various problems related to volatility and correlation dynamics.