基于SGT分布的贝叶斯统计推断的在险价值研究

Bayesian inference of VaR based on SGT distribution

在考虑金融数据的非正态分布的条件下,使用更接近市场实际的SGT(Skewed Generalizedt Distribution)分布取代正态分布,建立了基于SGT分布的VaR(Value-at-risk)计算模型,然后对于SGT分布的参数估计采用贝叶斯统计推断,提高了SGT分布的参数估计精度和VaR的度量准确性。并用上证指数对这个新方法做了实证检验,发现对于样本内的VaR的性能测试贝叶斯统计推断的结果和用SGT的最大似然估计结果相似,但都优于正态分布的结果,样本外的性能测试中贝叶斯统计推断的结果优于用SGT的最大似然估计和正态分布的结果.

Value-at-risk（VaR） is a financial risk measurement technique,which has become a standard for financial risk management.This paper proposed a new improved approach to Value at Risk（VaR） in a framework of Bayesian inference using the skewed generalized t distribution（SGT）.SGT distribution was used to substitute normal distribution,as it is closer to the true distribution of financial time series data.The SGT parameters were estimated via Bayesian interference formalism.This new approach was tested on a data set of Shanghai composite index.The results indicate that the VaR performs well on the in-sample evaluation while for the out-of-sample VaR test the Bayesian inference model is better than maximum likelihood estimation and normal distribution.