In this paper, we show that the recent integration of statistical models with
deep recurrent neural networks provides a new way of formulating volatility
(the degree of variation of time series) models that have been widely used in
time series analysis and prediction in finance. The model comprises a pair of
complementary stochastic recurrent neural networks: the generative network
models the joint distribution of the stochastic volatility process; the
inference network approximates the conditional distribution of the latent
variables given the observables. Our focus here is on the formulation of
temporal dynamics of volatility over time under a stochastic recurrent neural
network framework. Experiments on real-world stock price datasets demonstrate
that the proposed model generates a better volatility estimation and prediction
that outperforms mainstream methods, e.g., deterministic models such as GARCH
and its variants, and stochastic models namely the MCMC-based model
\emph{stochvol} as well as the Gaussian process volatility model \emph{GPVol},
on average negative log-likelihood
