Stochastic Volatility Modeling based on Doubly Truncated Cauchy Distribution and Bayesian Estimation for Chinese Stock Market

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Cai-feng Wang, Cong Xie, Zi-yu Ma, Hui-min Zhao
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引用次数: 0

Abstract

In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dtC model, a stochastic volatility (SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis for the parameters is made and Markov Chain Monte Carlo (MCMC) is used for computing the posterior estimates of the model parameters and forecasting in the empirical application of Shanghai Stock Exchange Composite Index (SSECI) with respect to the proposed SV-dtC model and two classic SV-N (SV model with Normal distribution) and SV-T (SV model with Student-t distribution) models. The empirical analysis shows that the proposed SV-dtC model has better performance by model checking, including independence test (Projection correlation test), Kolmogorov-Smirnov test(K-S test) and Q-Q plot. Additionally, deviance information criterion (DIC) also shows that the proposed model has a significant improvement in model fit over the others.

基于双截断柯西分布和贝叶斯估计的中国股市随机波动率建模
为了衡量股票市场中金融资产收益的不确定性,本文提出了一个新的模型,称为SV-dtC模型,这是一个假设股票收益具有双截尾柯西分布的随机波动率(SV)模型,同时考虑了经验分布的高峰和肥尾。在贝叶斯框架下,摘要针对上海证券交易所综合指数(SSECI)提出的SV-dtC模型和两个经典的SV-N(具有正态分布的SV模型)和SV-T模型,对模型参数进行了前后验分析,并用马尔可夫链蒙特卡罗(MCMC)计算了模型参数的后验估计和预测(SV模型与Student-t分布)模型。实证分析表明,通过模型检验,包括独立性检验(投影相关检验)、Kolmogorov-Smirnov检验(K-S检验)和Q-Q图,所提出的SV-dtC模型具有更好的性能。此外,偏差信息准则(DIC)也表明,与其他模型相比,所提出的模型在模型拟合方面有显著改进。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
70
审稿时长
3.0 months
期刊介绍: Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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