Numerics in production

Numerics in research code is one thing. Numerics in production — where prices feed risk reports, settlements, and capital calculations — is a different discipline. Reproducibility, regression testing, audit trails, performance monitoring, and graceful degradation are essential. This module covers what a quant developer ships when they 'add a model' to a production library.

Reproducibility

• Pin random seeds: every MC simulation should produce identical output when re-run.
• Pin library versions: numpy 1.26.0, not 'latest'. Floating-point ops can change subtly across versions.
• Pin platform: x86 vs ARM, Linux vs Mac can give last-bit differences. Document the test environment.
• Pin data: cache input snapshots so a model's output can be reproduced from inputs preserved at decision time.

Regression testing

Maintain a corpus of pricing tests: (model, parameters, expected price). On every code change, re-run the corpus and flag any test where price moves beyond tolerance. Distinguish:

• Intended changes: an explicit bug fix should change specific test values; document and accept.
• Unintended changes: a refactor or library upgrade should leave prices unchanged. Investigate any movement.
• Tolerance: typical pricing tolerance 1e-6 to 1e-10 relative; tighter for closed forms, looser for MC.

Performance monitoring

• Track latency per pricing call. Alert on regressions.
• Track standard error of MC pricers. Latency might be acceptable but accuracy degraded.
• Track solver-convergence diagnostics: iterations, residuals.
• Profile in production: where is time actually spent? Often the answer surprises — model-fit code is 5%, marshalling/serialisation is 50%.

Graceful degradation

When the high-accuracy method fails (timeout, numerical issue), what does the system do?

• Fall back to a coarser MC or PDE grid with explicit lower-accuracy flag.
• Use a closed-form approximation (Black-Scholes for an exotic) and flag the result.
• Return last-good price and flag stale.
• Refuse to price and flag for human review.

Never silently return an incorrect price. The path between a numerical failure and a trade ticket is the path along which firms lose money.

Calibration and re-calibration

Production models are calibrated to market data daily (or intraday). The calibration process — typically a non-linear optimisation — must converge reliably, deliver economically reasonable parameters, and produce stable risk numbers day-over-day. Common issues:

• Multiple local minima: pin to global by warm-starting from yesterday's solution.
• Boundary parameters: model jumping from interior to boundary changes risk numbers discontinuously.
• Calibration noise: small market-data perturbations producing big parameter changes. Regularise.
• Stress events: calibrating to crisis vol surfaces requires guardrails to prevent runaway parameters.

Audit trail

For every priced trade in a regulated context (basically anything that ends up on a bank's balance sheet), maintain: trade specification, model name and version, parameter snapshot, market data snapshot, pricing time, computed PV and Greeks, MC convergence diagnostics. This is a regulatory requirement and an operational lifesaver during audits or P&L investigations.

Testing the model

• Closed-form sanity checks: model prices reduce to known closed forms at limits (zero vol, zero rate, very long horizon).
• Cross-method validation: PDE price ≈ MC price ≈ tree price within tolerance.
• Put-call parity: P - C = K·exp(-rT) - F. Always check.
• Cross-strike monotonicity: call price strictly decreasing in K; put strictly increasing.
• No-arbitrage relations: gamma ≥ 0; calendar-spread non-negativity.

Versioning

Every model has a version string in its name (BS_v2_3). Deprecate old versions with grace periods. Maintain backward compatibility for already-traded books. When introducing a new version, validate on the historical corpus and document the differences in detail.

Handover documentation

When a quant developer leaves the firm, the next person should be able to: (1) run the model from a checkout, (2) understand the parameter conventions, (3) reproduce the regression tests, (4) calibrate to today's market. Documentation is the difference between a 2-week handover and a 6-month one.

Where to go next

• Stochastic Calculus: the theoretical foundation under all of this.
• Portfolio Theory and Optimization: the buy-side counterparts to derivatives quant.
• Python course: the language production numerics is most often written in (alongside C++).
• Engineering: software architecture, distributed systems, latency optimisation.