Value-at-Risk approximation of multivariate normal-inverse Gaussian distribution

• Main Authors: Szu-Fang Wang, 王思芳
• Other Authors: Yi-Ping Chang
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/15032720497214692153

碩士 === 東吳大學 === 商用數學系 === 92 === The financial return data has the character of fat tail. If we fit the financial return data in Normal distribution, the Value-at-Risk(VaR) will be misvalued. The multivariate normal-inverse Gaussian (MNIG) distribution arises as a normal variance-mean mixture with an inverse Gaussian (IG) mixing distribution. Its five parameters cam describe the kurtosis, location, scale, asymmetric and correlation of the data. Due to the complexity of the likelihood of MNIG distribution, direct maximization is difficult. An EM algorithm is provided for the maximum likelihood estimation (MLE) of the MNIG distribution. Beside ,this article fit the portfolio of financial return data in the MNIG distribution, multivariate normal distribution and multivariate student-T distribution. The result shows that the MNIG distribution can fit very well and estimate the VaR precisely.