I brought a neural network. The 1993 model won again.
Research note #2 · Neural pricing, part one · July 2026
Last note ended with GJR-GARCH — Glosten, Jagannathan and Runkle’s 1993 asymmetric volatility model, four parameters — beating a Markov state model we had named after ourselves. The obvious follow-up question: fine, but what about a neural network? Nonlinear interactions are exactly what a linear ladder cannot see. So we built one: a small MLP (~2,000 parameters), forecasting next-day range from the same information set plus the dealer-positioning state components, walk-forward with monthly refits, three-seed ensembles, early stopping. Same 1,794-day out-of-sample window, same gates as everything else.
| Forecaster | next-day range MAE (bps) |
|---|---|
| GJR-GARCH alone (4 parameters, 1993) | 41.6 |
| Full linear ladder (HAR + VIX + GJR) | 41.2 |
| Neural net, no state inputs | 63.4 |
| Neural net, with state inputs | 58.9 |
The network didn’t just fail to win — it lost significantly (Newey-West t = −4.37 on the error differential). Two thousand parameters, beaten by four, on ~3,500 daily observations. The states helped the network (58.9 vs 63.4) — consistent with everything we have measured about dealer positioning — but nothing rescues the architecture at this data scale. Daily-frequency volatility gives you about 250 observations a year; that is starvation rations for a neural net and a feast for a parsimonious recursion.
The same night, the same tool won somewhere else
Then we pointed the identical technology at a different shape of problem: approximating the Heston (1993 — good year) stochastic-vol pricing map, the “Deep Learning Volatility” program of Horvath, Muguruza & Tomas. Training data: 9,000 implied-vol surfaces generated by the model itself — dense, structured, unlimited.
| Gate | Result | |
|---|---|---|
| Surface accuracy (gate < 0.5 vol pts) | 0.23 vol pts MAE | PASS |
| Speedup vs direct integration (gate ≥ 100x) | ~45,000x | PASS |
| Skew sanity (rho < 0 ⇒ downward skew) | put wing 24.3%, calls 14.3% | PASS |
Same architecture family, opposite verdicts, one lesson: neural networks are not a upgrade you sprinkle on a forecast. They win where data is dense and structured — an option surface is thousands of simultaneous, arbitrage-linked quotes — and lose to forty-year-old econometrics where data is scarce and noisy. Anyone selling you a neural net fitted to one daily time series is selling you the 63.4 in the first table.