  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.
