  Estimating value-at-risk on time series data with possibly heteroscedastic
dynamics is a highly challenging task. Typically, we face a small data problem
in combination with a high degree of non-linearity, causing difficulties for
both classical and machine-learning estimation algorithms. In this paper, we
propose a novel value-at-risk estimator using a long short-term memory (LSTM)
neural network and compare its performance to benchmark GARCH estimators.
  Our results indicate that even for a relatively short time series, the LSTM
could be used to refine or monitor risk estimation processes and correctly
identify the underlying risk dynamics in a non-parametric fashion. We evaluate
the estimator on both simulated and market data with a focus on
heteroscedasticity, finding that LSTM exhibits a similar performance to GARCH
estimators on simulated data, whereas on real market data it is more sensitive
towards increasing or decreasing volatility and outperforms all existing
estimators of value-at-risk in terms of exception rate and mean quantile score.
