深度随机波动率模型

摘要：

金融资产收益的波动性可以用来衡量金融市场的风险。本文在深层潜变量模型的基础上提出了一个深层随机波动率模型。它使用灵活的深度学习模型来自动检测未来波动率对过去收益率、过去波动率和随机噪声的依赖性，从而提供灵活的波动率模型，而无需手动选择特征。我们开发了一个可扩展的推理和学习算法的基础上变分推理。在实际数据分析中，DSVM优于几个流行的替代波动率模型。此外，DSVM的预测波动率提供了一个更可靠的风险度量，可以更好地反映金融市场的风险，与美国股票市场上的庞大数据集相比，当市场变得更有风险时，可以更快地达到更高的水平，当市场更稳定时，可以更快地达到更低的水平。

英文摘要：

Volatility for financial assets returns can be used to gauge the risk for financial market. We propose a deep stochastic volatility model (DSVM) based on the framework of deep latent variable models. It uses flexible deep learning models to automatically detect the dependence of the future volatility on past returns, past volatilities and the stochastic noise, and thus provides a flexible volatility model without the need to manually select features. We develop a scalable inference and learning algorithm based on variational inference. In real data analysis, the DSVM outperforms several popular alternative volatility models. In addition, the predicted volatility of the DSVM provides a more reliable risk measure that can better reflex the risk in the financial market, reaching more quickly to a higher level when the market becomes more risky and to a lower level when the market is more stable, compared with the commonly used GARCH type model with a huge data set on the U.S. stock market.

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