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首页> 外文期刊>The econometrics journal >A stochastic volatility model with random level shifts and its applications to S&P 500 and NASDAQ return indices
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A stochastic volatility model with random level shifts and its applications to S&P 500 and NASDAQ return indices

机译：具有随机水平变动的随机波动率模型及其在标普500和纳斯达克指数中的应用

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摘要

This paper proposes a framework for the modelling, inference and forecasting of volatility in the presence of level shifts of unknown timing, magnitude and frequency. First, we consider a stochastic volatility model comprising both a level shift and a short-memory component, with the former modelled as a compound binomial process and the latter as an AR(1). Next, we adopt a Bayesian approach for inference and develop algorithms to obtain posterior distributions of the parameters and the two latent components. Then, we apply the model to daily S&P 500 and NASDAQ returns over the period 1980.1-2010.12. The results show that although the occurrence of a level shift is rare, about once every 2 years, this component clearly contributes most to the variation in the volatility. The half-life of a typical shock from the AR(1) component is short, on average between 9 and 15 days. Interestingly, isolating the level shift component from the overall volatility reveals a stronger relationship between volatility and business cycle movements. Although the paper focuses on daily index returns, the methods developed can potentially be used to study the low-frequency variation in realized volatility or the volatility of other financial or macroeconomic variables.
机译：本文提出了一个在时间，幅度和频率未知的水平移动下对波动率进行建模，推断和预测的框架。首先，我们考虑一个随机的波动率模型，它既包含一个水平移位又包含一个短内存成分，前者建模为复合二项式过程，后者建模为AR（1）。接下来，我们采用贝叶斯方法进行推理，并开发算法以获得参数和两个潜在分量的后验分布。然后，我们将该模型应用于标准普尔500指数和纳斯达克每日1980.1-2010.12的回报。结果表明，尽管很少发生电平移动，但大约每2年一次，但该分量显然是导致波动率变化的最大因素。 AR（1）组件产生的典型冲击的半衰期很短，平均在9到15天之间。有趣的是，从总体波动率中分离出水平移动成分可以揭示波动率与商业周期变动之间的更强的关系。尽管本文关注的是每日指数收益，但开发的方法可以潜在地用于研究实际波动率或其他金融或宏观经济变量的波动率的低频变化。

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