Neural Surrogate for a Rough-Volatility Pricer: Pricing Versus Risk Approval
Your bank's front-office quant team has replaced a 200,000-path Monte Carlo pricer with a neural-network surrogate. The underlying model is a rough-volatility stochastic-volatility model with six parameters. The network is a four-hidden-layer MLP trained on 500,000 Latin-hypercube parameter draws, mapping parameters and strike/maturity to implied volatility. In-sample relative RMSE is 0.15% and median pricing time falls from 40 ms to 0.2 ms. Risk control now wants to use the surrogate for intraday CVA and VaR on a $4bn book, where positions are revalued every 15 minutes. During validation, the team evaluates the network on a stress grid with vol-of-vol doubled and mean reversion halved: relative error rises to 7%, and 3% of points violate no-arbitrage, producing negative implied densities. Internal model policy requires a documented domain of validity and a fallback path. The CRO asks whether the surrogate can be approved for pricing, for risk, or neither.
1. Distinguish the validation evidence required for client pricing versus internal risk use, and decide whether to approve the surrogate for either.
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The two uses have different loss functions. For pricing, the relevant question is pointwise accuracy and arbitrage consistency inside the traded domain: a small median error is not enough, because a single mispriced strike can be exploited or mis-booked. Acceptance should use maximum or 99.9th-percentile error, checks of monotonicity and convexity in strike, and an independent test set. The 0.15% in-sample RMSE does not establish any of this.
For risk, the relevant question is tail and stress behaviour. VaR and CVA depend on the joint behaviour of volatility and price in extreme regions, exactly where the network's 7% error and 3% arbitrage violations appear. A surrogate that is accurate on the training cube but diverges when vol-of-vol doubles is extrapolating precisely where the bank needs it most, and CVA introduces wrong-way-risk sensitivity to that error.
Decision: conditional approval for pricing only, restricted to an explicitly certified parameter and strike domain, with automated fallback to Monte Carlo. Reject for risk use until the network is retrained and independently validated on stress regions and shown to be arbitrage-free there. Median accuracy on the training distribution is not evidence of tail validity.
2. Design the controls that would make the surrogate usable: domain-of-validity check, fallback, and acceptance metrics.
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A workable control set has four layers:
- Domain check at inference. Compute a distance of the input vector from the training distribution (Mahalanobis distance, convex-hull membership, or ensemble disagreement). If the input is outside the certified region, route to Monte Carlo automatically and log the event.
- Fallback trigger. Even inside the domain, fall back if predicted Greeks are unstable, if the implied density is negative, or if ensemble variance exceeds a threshold. The fallback must be fast enough for the 15-minute revaluation cycle, which may require a reduced-path MC rather than the full 200,000 paths.
- Arbitrage repair. Project the predicted surface onto an arbitrage-free family (for example SSVI or a monotone-convex fit) and record the size of the projection as a model-risk metric.
- Acceptance metrics. Set explicit gates: maximum relative error in-domain below, say, 10 bps; 99.9th-percentile error below a stated bound; zero negative densities on the test grid; bounded delta and vega error; and stable performance across stress sub-domains. Retrain with stress-augmented samples and an arbitrage penalty, then rerun independent validation.
Ongoing monitoring should track the fraction of fallbacks, projection size, and error against a random MC audit sample.
3. Quantify why a 7% volatility error may be material for a $4bn intraday VaR and CVA book even if the median pricing error is small.
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Option values are nonlinear in volatility, so error propagates through vega and higher Greeks rather than through the median price alone. If the book carries substantial vega, a 7% error in the volatility input can shift the mark-to-market distribution by a comparable fraction of vega-weighted exposure. For a book with, say, $80m one-day 99% VaR, a systematic volatility error of that size can move the VaR estimate by several million dollars, and the error is one-sided in stress because the network under-reacts outside its training cube.
CVA adds a second channel. Exposure profiles are generated under the same model; if the surrogate misstates volatility in stress, the expected positive exposure and the correlation between exposure and counterparty default (wrong-way risk) are both biased. The 3% of points with negative implied densities are especially dangerous because they can produce negative tail probabilities and invalid scenario P&L.
The median error of 0.15% is therefore irrelevant to the risk decision. What matters is the error conditional on being in the tail and in stress, and there the validation evidence is 7% with arbitrage violations. Intraday revaluation every 15 minutes also means the error is repeated roughly 26 times per trading day rather than averaged away.