  We propose a novel structural estimation framework in which we train a
surrogate of an economic model with deep neural networks. Our methodology
alleviates the curse of dimensionality and speeds up the evaluation and
parameter estimation by orders of magnitudes, which significantly enhances
one's ability to conduct analyses that require frequent parameter
re-estimation. As an empirical application, we compare two popular option
pricing models (the Heston and the Bates model with double-exponential jumps)
against a non-parametric random forest model. We document that: a) the Bates
model produces better out-of-sample pricing on average, but both structural
models fail to outperform random forest for large areas of the volatility
surface; b) random forest is more competitive at short horizons (e.g., 1-day),
for short-dated options (with less than 7 days to maturity), and on days with
poor liquidity; c) both structural models outperform random forest in
out-of-sample delta hedging; d) the Heston model's relative performance has
deteriorated significantly after the 2008 financial crisis.
