基于状态空间的贝叶斯跳跃厚尾金融随机波动模型研究

Bayesian Analysis of Heavy-tailed Financial Stochastic Volatility Models with Jumps Based on its State Space

针对金融市场中跳跃特征的刻画问题,提出了贝叶斯跳跃厚尾随机波动模型。通过随机波动模型的结构分析和状态空间转换,设计了模型参数估计的MCMC算法,利用Kalman滤波和高斯模拟平滑方法估计模型的潜在波动,运用贝叶斯因子对随机波动类模型进行比较分析,并利用中国和美国的股市收益数据进行实证分析。研究结果表明:在刻画中、美两国股票市场的波动特征方面,跳跃厚尾随机波动模型要明显优于厚尾随机波动模型和标准随机波动模型,并且金融危机背景下的中国和美国股票市场都具有明显的波动持续性以及跳跃特征。

This paper proposes the Bayesian heavy-tailed stochastic volatility models with jumps to describe the jumps characteristics in financial market.In terms of the volatility models＇ structure and their state space transition,we construct a Markov Chain Monte Carlo algorithm to estimate parameters,utilize Kalman filters and Gaussian simulation smoother to analyze the latent volatility implied in models,and compare volatility models through Bayesian factors.Then the suggested approach is applied to analyze the volatility character of the stock market in China and America.The results show that the jump character is significant both in China and America stock market,and the heavy-tailed stochastic volatility model with jumps is superior to the standard volatility model in depicting volatility character.