Simulator & Validation Reference

A regime-switching stochastic-volatility model — not a replay of history and not random noise. A market moves through four regimes — BULL · SIDEWAYS · BEAR · CRISIS — and each imposes a characteristic drift and volatility level. The path is not locked to one regime: it transitions between them along a matrix estimated from real index history (1999–2025), which reproduces the historical regime distribution (roughly 40 / 39 / 11 / 10 %), so the alternation of calm and stressed stretches matches how real markets behave.

Volatility clustering is produced by a persistent volatility process layered on that regime oscillation: a turbulent day raises the volatility state for the days that follow (an AR(1)-like memory, roughly a four-day half-life), so large moves arrive in clusters rather than spread evenly. This is the single most universal property of real returns, and it is the model’s load-bearing feature — the admissibility gate in §3 enforces it.

Per-asset character comes from calibrating each asset to its own price history — its volatility level, tail thickness, drawdown profile and regime mix — not from hand-set knobs. The per-asset targets are the reference bands in §4.

Every asset is calibrated to its own historical statistics, and a simulated path is admissible only when its measured properties fall inside that asset’s bands (§4) — not a generic default. Clustering, volatility and tail thickness differ markedly across assets, so a "low" clustering figure on gold or crypto can be asset-appropriate rather than a defect.

Coverage. The example strategy reports span seven assets — SPY, QQQ, GOLD, WTI, BTC, ETH (VIX is held back — see §9). The live portfolio-stress substrate covers four — SPY, TLT, GOLD, BTC — the set for which the cross-asset coupling (§6) is calibrated.

A synthetic regime is only a valid market test if it reproduces the most fundamental stylized fact: positive volatility clustering (the lag-5 autocorrelation of absolute returns, "acf5", per Cont, 2001). A scenario with zero or negative clustering is an anti-market — a strategy "optimised" against it is optimising against a simulation artifact. So acf5 is a hard gate: every deployable regime must clear it, against the asset’s own historical band (clustering is asset-specific — see §4).

This gate is load-bearing: clearing it is the difference between a plausible market and noise. Every regime in the catalog below passes it, measured against its own asset’s band.

The 2022 hedge break is modelled the way it actually happened: not as a spike in day-to-day correlation, but as a shared drawdown — on a rate shock, equities and long Treasuries both lose ground together (a 60/40 takes roughly a −14 % worst-episode drawdown in that scenario, versus the −10 % a drawdown-stop would have held it to). That is the "60/40 loses both legs" failure a stress tool must show. Honest boundary: the model adds value in the regime-conditional correlation and the joint-crash tail dependence — single-asset daily marginals are at parity with cheap baselines, and the SPY–BTC crisis magnitude is undershot. The full numeric comparison against a Gauss-copula baseline is on the verifiability page.

OHLC bars hide the intra-bar order of events: when price touches both a stop-loss and a take-profit within the same bar, the execution order is ambiguous. Many engines resolve that optimistically. This engine applies the methodology of Löw, Maier-Paape & Platen (2015), defaulting to worst-case execution (the unfavourable order is assumed). Best-case and ignore modes are available as explicit bounds. The conservative default yields lower-bound performance estimates rather than optimistic ones.