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feat: Jump Lab — Merton & Bates calibrated to the Deribit smile

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- core/jump_models.py: Black-76 helpers and implied vol; Merton series in
  forward form (Poisson(lambda T) weights, F_n = F e^{-lambda k T}(1+k)^n);
  Bates characteristic function in the 'little Heston trap' form with COS
  pricing (puts + parity) and risk-neutral density; vega-weighted bounded
  least-squares calibration across expiries; jump statistics (crash-jump
  odds, jump share of variance) and density vs lognormal.
- GET /api/jumps/calibrate/{BTC,ETH}: fits both models to every Deribit
  expiry from the Vol Lab feed (cached 30 min, 503 when Deribit is down).
- POST /api/jumps/merton: manual Merton smile/density for metals and FX
  event and gap risk.
- Jump Lab tab: fit KPIs, market vs Merton vs Bates smiles per expiry,
  30-day density, parameter table, and a hand-off of the calibrated jumps
  to Hedge Lab (store.hedgeJump -> Hedge Lab defaults to the jump model).
- 5 tests: Black/Merton/Bates limits, parity, density mass and martingale,
  exact-MC Merton and Euler-MC Bates checks, parameter recovery (clean and
  noisy), Merton-vs-Bates misspecification, endpoints.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01FpiqUMAyo4RL5DdQHMWbwE
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@@ -42,6 +42,7 @@ NEXUS TERMINAL is a Bloomberg-style web application for professional forex optio
| **Vol Forecast & Regime (AI)** | HAR-RV (weekend-aware for crypto), GJR-GARCH and gradient-boosting forecasts of 1D/1W/1M vol, rolling out-of-sample QLIKE leaderboard with an inverse-QLIKE ensemble, 2-state HMM regime detection, and a forecast-vs-Deribit-implied rich/cheap signal |
| **Hedge Lab** | Monte Carlo delta-hedging / gamma-scalping P&L of your portfolio: realised vs implied vol, GBM / Merton jumps / historical block bootstrap, weekend gaps for 24/5 markets, time or delta-band hedging, transaction costs and carry, with Derman-Kamal and Leland benchmarks and a hedge-frequency risk-vs-cost sweep |
| **Cross-Asset Desk** | Gold · silver · BTC · ETH · EURUSD · DXY · US10Y · WTI correlation matrices (30D/90D/1Y/EWMA) with a correlation-break monitor; gold/silver ratio z-scores, OU half-life, Engle-Granger cointegration and Kalman hedge ratio; Margrabe outperformance-option pricer with correlation sensitivity |
| **Jump Lab** | Merton and Bates (Heston + jumps, COS pricing) calibrated to every live Deribit BTC/ETH expiry: model-vs-market smiles, fit RMSE, jump intensity/size, jump share of variance, crash-jump odds, 30-day risk-neutral density vs lognormal; manual Merton for metals/FX event and gap risk; one-click hand-off of jump parameters to Hedge Lab |
### Live Intelligence