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1da2fa19c6
- M3 hub: add L3 invariant (360:1 minimum sim speed), six-horizon time table - M3a: add Heston stochastic vol, rough volatility (fBM), HMM regime detection, DCC-GARCH copula, jump-diffusion; six-horizon mapping - M3b: add Hegselmann-Krause bounded confidence, complex contagion, bandit- replicator hybrid, MFG (HJB+FP), pump-and-dump 3-type ABM; six-horizon mapping - M3c: add six-horizon time table - M3d: add Kolokoltsov adversarial (non-linear FP + WENO), DSMFG bilevel optimization, cross-chain adversarial arbitrage; six-horizon mapping - M3e: add kinked lending rate model, DeXposure inter-protocol credit network, composable yield optimizer; six-horizon mapping - M3f: add MFG for validator populations, six-horizon time table - M3g: add Almgren-Chriss optimal execution, six-horizon mapping - CLAUDE.md: add subagent productivity note Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
109 lines
6.9 KiB
Markdown
109 lines
6.9 KiB
Markdown
# M3a — Statistical & quantitative sims
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## 1. Component
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Pure statistical simulation: **Monte Carlo methods, Bayesian inference, time-series forecasting,
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stochastic volatility, regime detection, and cross-asset correlation**. The mathematical backbone
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— no game theory, no sociology, just the numbers. Operates across **six concurrent time horizons**
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(tick → hourly → daily → weekly → monthly → annual → 5-year). Pops in this sim represent
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**stochastic sample paths**, not behavioral agents.
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## 2. Status / certainty
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DESIGN-FIRST · ABSENT. Core quant methods C5 (GBM, GARCH, ARIMA — textbook). Heston stochastic
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volatility C5 (closed-form characteristic function; industry standard since 1993). Rough
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volatility C4 (Gatheral et al. 2018, heavily cited; crypto implementations exist). HMM regime
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detection C4 (established; crypto-specific copula hybrids emerging 2023–2024). Almgren-Chriss
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execution C5 (industry standard since 2001). Jump-diffusion C5 (Merton 1976). Parameterization
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for crypto markets C1.
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## 3. Language & location
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TBD · `src/economy/sims/statistical/`. Python (NumPy/SciPy), Julia, or R for numerical
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computing. Needs efficient matrix operations, SDE solvers, and distribution sampling. Fractional
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Brownian motion generation requires specialized libraries (e.g. `fbm` in Python, or spectral
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methods).
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## 4. Does / does-not
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- **Does:** run Monte Carlo price simulations (GBM, Merton jump-diffusion, Heston stochastic
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volatility); model volatility surface via **Heston SDE**:
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$dS_t = \mu S_t dt + \sqrt{\nu_t} S_t dW_t^S$,
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$d\nu_t = \kappa(\theta - \nu_t)dt + \xi\sqrt{\nu_t} dW_t^\nu$
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with $\text{corr}(dW^S, dW^\nu) = \rho$ (mean-reversion speed $\kappa$, long-run variance
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$\theta$, vol-of-vol $\xi$); model **rough volatility** via fractional Brownian motion
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$dS_t = \mu dt + \sigma_t dB_t^H$ with Hurst exponent $H \approx 0.4$ capturing
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antipersistent microstructure (Gatheral et al. 2018); detect **regime transitions** via
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Hidden Markov Model: $r_t | s_t \sim \mathcal{N}(\mu_{s_t}, \sigma^2_{s_t})$,
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$s_t \in \{\text{Bull, Neutral, Bear}\}$ with Viterbi filter updating in <5ms per tick;
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model **cross-asset tail dependence** via DCC-GARCH copula hybrid:
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$dQ_t/dt = a \cdot (\bar{S} - Q_t) + b \cdot (\varepsilon_t \varepsilon_t^T - Q_t)$
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with $t$-Copula for fat-tailed spillovers (BTC→alts); Bayesian parameter estimation from
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live data (M2); time-series forecasting (ARIMA, GARCH for volatility clustering); Value-at-Risk
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and Expected Shortfall; produce bounded predictions with confidence intervals.
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- **Does-not:** model human behavior (M3b does); model protocol mechanics (M3c–M3f do);
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trade or recommend (Traders do); optimize execution routing (M3g does using our vol estimates).
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## 5. Interface contract
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- Implements `query(PredictionQuery) -> BoundedPrediction` per M3 hub.
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- **Output bounds:** statistical confidence intervals (CI from Monte Carlo), Heston variance
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bands (from $\nu_t$ process), rough-vol forecast cones, regime-conditional intervals.
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- **Time-horizon mapping** (all run concurrently):
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| Horizon | Primary models | Update cadence |
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|---------|---------------|----------------|
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| Tick–hourly | Rough vol ($H \approx 0.4$), HMM regime filter, realized variance | Every tick |
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| Daily | Heston vol surface, GARCH, DCC correlation | Every bar close |
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| Weekly–monthly | Jump-diffusion Monte Carlo, regime-conditional forecasts | Hourly roll |
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| Annual–5yr | SDE mean-reversion long-run $\theta$, macro regime priors | Daily roll |
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- Examples:
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`{ value: 1847.30, lower_bound: 1790.15, upper_bound: 1905.60, confidence: 0.95,
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time_horizon: "24h", sim_type: "statistical" }` — 95% CI on ETH price.
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`{ value: 0.72, lower_bound: 0.58, upper_bound: 0.89, confidence: 0.90,
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time_horizon: "1h", sim_type: "statistical" }` — Heston instantaneous vol $\sqrt{\nu_t}$.
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`{ value: "bear", lower_bound: null, upper_bound: null, confidence: 0.83,
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time_horizon: "current", sim_type: "statistical" }` — HMM regime state.
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- **Prediction types:** `price_forecast`, `volatility_surface`, `var_calculation`,
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`correlation_matrix`, `regime_state`, `rough_vol_estimate`, `jump_intensity`.
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- Calibration: ingests `price_tick` and `dex_pool_state` from M2 Data Feeds.
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## 6. Dependencies & stubs
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- M2 Data Feeds — price history for calibration; *stub:* canned price series.
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- M3 Sims hub — lifecycle management; *stub:* manual init.
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## 7. Invariants / laws
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- **L1 (C5):** bounds are **statistical confidence intervals** — derived from the model's
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distribution, not hand-picked. The confidence level (e.g. 0.95) is explicit in the output.
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- **L2 (C5):** **six time horizons run concurrently** — tick-level rough vol, hourly regime
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detection, daily Heston surface, weekly Monte Carlo, annual mean-reversion, and 5-year macro
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forecasts coexist; none blocks the others.
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- **L3 (C4):** model parameters are **re-estimated on each calibration** from live data — no
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stale parameters carried across regime changes. Regime transitions trigger immediate
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re-estimation of conditional parameters.
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- **L4 (C4):** the **Heston correlation $\rho$ between price and vol** is a fitted parameter,
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never assumed — crypto assets exhibit leverage effects different from equities.
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- **L5 (C4):** rough volatility Hurst exponent $H$ is **estimated from realized variance**, not
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fixed — $H$ varies across assets and regimes (Gatheral et al. 2018).
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## 8. Build steps
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1. Implement geometric Brownian motion Monte Carlo (simplest price sim).
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2. Add GARCH volatility estimation.
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3. Implement Heston SDE solver (Euler-Maruyama with full truncation for $\nu_t \geq 0$).
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4. Add Merton jump-diffusion (Poisson jumps + GBM).
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5. Implement rough volatility via fractional BM with rolling Hurst estimator.
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6. Implement HMM regime detector (3-state Viterbi filter).
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7. Add DCC-GARCH copula for cross-asset correlation.
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8. Wire M2 price data → Bayesian parameter re-estimation.
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9. Implement multi-horizon `BoundedPrediction` output with CIs.
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## 9. Tests
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Monte Carlo: N sample paths produce a distribution with correct mean/variance. CI: 95% interval
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contains true value ≥ 95% of the time on historical backtest. GARCH: volatility clusters detected
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in synthetic data. Heston: implied vol smile reproduced for known parameters. Rough vol: Hurst
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exponent recovered from synthetic fBM paths. HMM: regime transitions detected within 15–60s on
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synthetic regime-switching data. Copula: tail dependence captured (BTC crash → alt crash
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correlation spike). Jump-diffusion: fat tails reproduced. Calibration: new data shifts parameter
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estimates. Multi-horizon: all six horizons produce concurrent outputs.
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## 10. Open items
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- Heston calibration method (characteristic function inversion? particle filter?).
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- Rough vol computational cost (fBM generation is O(N²) naively; FFT methods needed).
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- HMM state count (3 sufficient? 4+ for crypto with "mania" regime?).
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- Which copula family for tail dependence ($t$-copula? Clayton? Joe?).
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- Computational budget per horizon (GPU for Monte Carlo paths?).
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