基于贝叶斯分位数回归的市场风险测度模型与应用

Measure Market Risk Based on Bayesian Quantile Regression Model with an Application

对具有递归或非递归表达形式的一般分位数回归模型,基于不对称拉普拉斯分布提出了贝叶斯推理框架。指出不对称拉普拉斯分布的尺度参数在估计中应该被参数化,否则将导致其方差存在非零最小值的限制。给出选择尺度参数和模型参数先验分布的条件,保证参数后验分布是真实概率分布,并采用马尔科夫链蒙特卡罗模拟方法进行参数估计。对深证成分指数的实证研究表明,不对称绝对值和斜率分位数回归模型比间接GARCH和FIAPARCH模型更好地描述了深证成分指数的风险特征,在不同的置信水平下,深圳股市消息对市场风险具有强度不同的不对称性冲击。动态分位检验和后验测试支持分位数回归模型可以对金融数据进行高置信水平的市场风险测量和探索风险的演化模式。

In the paper, based on asymmetric Laplace distribution, Bayesian inference with Markov chain Monte Carlo simulation is recommended to estimate general quantile regression model; no matter the quantile equation has a recursive or non-recursive specification. We indicate that scale parameter in asymmetric Laplace distribution should be parameterized in Bayesian inference for quantile-based model. Treating scale parameter as a fixed constant subjectively will impose a positive non-zero minimum variance on data, which is improper in real applications. A new theorem that can ensure the posterior distributions of estimated parameters are always proper is given,and Markov chain Monte Carlo simulation is adopted to estimate the parameters. By an empirical analysis to Shenzhen Component Index, it is found the asymmetric absolute value and slop specification of quantile is superior to the indirect GARCH and FIAPARCH models in explaining the nature of market risk in Shenzhen Stock Exchange. It is also shown the one-order lagged bad or good price news has significant different asymmetric impacts on the market risk under different confidence levels. It is proved that quantile regression model is a valid approach to measure market risk at extreme probability level for financial data and explore the risk evolution patterns.