Model risk · inventory and monitoring

Value: links to the panel that shows the evidence; the bar under it runs from 0 through the OK, watch and breach bands of the limits printed beneath it, with a tick at the value. History: one dot per stored session, oldest first, coloured by today’s limits; stored sessions, irregular spacing; today’s limits applied retroactively. A dot is a measurement on that session, not a point of a control chart.

How to read the status

OK, WATCH and BREACH compare the value with the limits in the same row (green ≤ the first limit, watch ≤ the second, breach above); every status also carries a word and a glyph, so colour is never the only cue. INFO rows are reported, not limited: the Feller condition is a diagnostic here, not a no-arbitrage requirement. A BREACH is not an outage: it marks where the model is weakest, which the linked page explains. The rows run worst first (breach, watch, OK, informational), and within a status in inventory order.

The canonical model inventory: every model the system runs or keeps, with its use, inputs, outputs and known limitations. The IDs and names are the ones the validation pack uses (docs/model_validation/README.md §1); test_dashboard.py checks that every pack ID is here under the same name. Tier: production = feeds a published number every session; backtest = feeds the backtest; research = kept for comparison or as a negative result, feeds nothing. Materiality: how much a published number depends on the model (high: a headline number or its sign; medium: a secondary published number; low: diagnostics only). test_dashboard.py checks that every listed module and artifact path exists.

Units and signs

Vol levels

in %: e.g. an implied or realised vol of 20.00% (σ = 0.2000).

Vol differences and errors

in vol pts, percentage points of vol: 21.00% − 20.00% = 1.00 vol pts.

VIX-family levels

VIX, VIX9D, VIX3M, VIX6M and VVIX in index pts, never '%': e.g. VIX 20.00.

Quote residuals

in half-spreads (|z|): 1 is the edge of the quoted bid–ask.

Money

$ per SPX contract (×100 multiplier) where a row says so; $ with k / M suffixes; backtest P&L is marked to model at β·VIX on collateral assumed to earn T-bills separately, so it is an excess return.

Signs

model − market (a positive bias is a model above the mid), implied − realised (a positive premium is implied above realised), replicated − Cboe close; each table's caption restates its sign.

Moneyness and maturity

ln(K/F) against the expiry's parity forward F; days are calendar days to expiry unless a column says NYSE sessions; 1M = 30 days.

Probabilities

risk-neutral where the Surface prints them (they price claims; they are not forecasts).

Terms

half-spread

Half a quote's bid–ask in implied-vol terms, (ask IV − bid IV)/2. Residuals are measured in it; the surface fits divide each residual by it, floored at 0.05 vol pts. Units: vol pts · used on Surface, Calibration, Overview · joint_vol_calibration/surface/essvi.py (fit_essvi, h_floor)

|z| absolute residual in half-spreads

|model IV − mid IV| / half-spread of one quote; |z| ≤ 1 is inside the quoted bid–ask. Scorecards report its median over a model's out-of-sample quotes. Units: half-spreads · used on Surface, Calibration, Overview · dashboard/desk_artifacts.py (residual_stats)

vol pts volatility points

A difference of two vols in percentage points: 21.00% against 20.00% is 1.00 vol pts. RMSE, bias, RR, BF and premia are in vol pts; vol levels are in %. Units: percentage points of vol · used on every page · the house style above

index pts index points

The unit of a VIX-family level and its errors (VIX 20.00 is 20.00 index pts), and of SPX option prices (×100 for $ per contract). Units: index points · used on Overview, Calibration, Surface, Model Risk · the house style above

ATMF at-the-money-forward vol

The implied vol of the SVI-cal slice at the forward strike, ln(K/F) = 0. Units: % · used on Surface · dashboard/desk_surface.py (delta_grid)

RR25 25-delta risk reversal

Vol of the 25Δ call − vol of the 25Δ put, at undiscounted forward delta on the slice's own vol (not premium-adjusted); negative: puts over calls. Units: vol pts · used on Surface · dashboard/desk_surface.py (delta_grid)

BF25 25-delta butterfly

(25Δ call vol + 25Δ put vol)/2 − ATMF, same deltas as RR25. Units: vol pts · used on Surface · dashboard/desk_surface.py (delta_grid)

ATM skew

∂σ/∂ln(K/F) at the forward, k = ln(K/F) = 0; for an SVI-cal slice w′(0)/(2·√(w(0)·T)) in decimal vol. Calibration and the Overview quote it per unit k; the Surface grid scales it to vol pts per 0.1 of k, ×10: −1.50 per unit k is −15.0 vol pts per 0.1 of k. Negative: puts over calls. Units: vol per unit ln(K/F); vol pts per 0.1 of ln(K/F) on the Surface grid · used on Surface, Calibration, Overview · dashboard/desk_surface.py (svi_atm_skew, SKEW_UNIT_K)

SVI-cal calendar-ordered SVI surface

The calendar-ordered SVI surface: one raw-SVI slice (a, b, ρ, m, σ) per listed expiry, each with a butterfly certificate (Durrleman's g ≥ 0, so its density is non-negative). Units: — · used on Surface, Calibration, Overview · joint_vol_calibration/surface/svi.py

eSSVI extended surface SVI

One extended-SSVI surface fitted jointly to every expiry, its parameters constrained against static arbitrage. Units: — · used on Surface · joint_vol_calibration/surface/essvi.py

out of sample

Quotes a model was not fitted to: the surfaces hold out alternate strikes of each expiry; Heston is fitted to its anchors and scored on every other quote. Units: — · used on Surface, Calibration, Overview · data_store/surface/ (surface.json fit_set)

PSR probabilistic Sharpe ratio

Bailey & López de Prado (2012): P(true Sharpe > 0) given the sample Sharpe, its length, skew and kurtosis, assuming IID returns (the bootstrap intervals are the primary inference). Units: probability · used on Research · joint_vol_calibration/stats/sharpe.py

DSR deflated Sharpe ratio

Bailey & López de Prado (2014): the PSR against the expected maximum Sharpe of N̂ trials, N̂ = ρ̄ + (1 − ρ̄)·M for M trials with average pairwise correlation ρ̄. Units: probability · used on Research · joint_vol_calibration/stats/sharpe.py

SPA superior predictive ability test

Hansen (2005), the studentised and recentred Reality Check (arch.bootstrap.SPA). H0: no strategy has a positive expected excess return; the 'consistent' p-value is the headline. Units: p-value · used on Research · joint_vol_calibration/stats/multiple_testing.py

StepM stepwise multiple testing

Romano & Wolf (2005) via arch.bootstrap.StepM: which strategies, if any, beat cash with family-wise error rate ≤ the test size. Units: — · used on Research · joint_vol_calibration/stats/multiple_testing.py

PBO probability of backtest overfitting

Bailey, Borwein, López de Prado & Zhu (2017), by CSCV: the share of splits in which the strategy with the best in-sample Sharpe ranks at or below the median out of sample (logit of its relative rank ≤ 0). Units: probability · used on Research · joint_vol_calibration/stats/multiple_testing.py

CSCV combinatorially symmetric cross-validation

The PBO's resampling: the sample is cut into S blocks and every combination of S/2 blocks serves once as the in-sample set, its complement as the out-of-sample set. Units: — · used on Research · joint_vol_calibration/stats/multiple_testing.py

MCS model confidence set

Hansen, Lunde & Nason (2011) via arch: the forecasts not rejected as worse than the best at the test size, with a p-value per forecast. Units: p-value · used on Research · joint_vol_calibration/stats/forecast.py

QLIKE quasi-likelihood loss

QLIKE(y², f) = y²/f − log(y²/f) − 1 on annualised variance (Patton 2011: robust to the noise in a realised-variance proxy); lower is better. Units: — · used on Research, Model Risk · joint_vol_calibration/stats/forecast.py

Holm Holm step-down adjustment

Holm (1979) step-down adjusted p-values: family-wise error control across the tests named beside it. Units: p-value · used on Research · joint_vol_calibration/stats/nulls.py

z_vrp VRP z-score

S4's z-score of VRP = VIX − 20-day realised vol (decimal vol, rebuilt as vix × (1 − 1/fear_premium)): (VRP − its 252-session mean) / its 252-session sd. Units: sd · used on Research · joint_vol_calibration/signals/signal_engine.py

RV21 21-session realised vol

100·√(252/21 · Σ r²) over 21 daily SPX close-to-close log returns: trailing (known at the close) or forward (the next 21 sessions). Units: % · used on Overview, Research · dashboard/desk_market.py

rv₂₀ the rule's 20-session realised vol

100·√(252 · mean r²) over the last 20 daily SPX log returns (at least 15 present): the realised vol the regime rule compares with VIX. It differs from RV21 by its window (20 against 21 sessions) and its minimum count, not by method. Units: % · used on Overview · joint_vol_calibration/signals/regime_classifier.py (_label_rv)

R0–R2 rule regime labels

The rule's regime labels: R0 long gamma, R1 short gamma, R2 vomma active (VVIX above its threshold at the close); the backtest reads them lagged one session. Units: label · used on Overview, Research · joint_vol_calibration/signals/regime_classifier.py (build_rule_label_frame)

vomma P&L ratio

½·vomma·Δσ² / (vega·|Δσ|) = ½·d₁·d₂·|Δσ|/σ for a vol move Δσ: the second-order vol P&L against the first; a node is flagged convexity-dominated above the monitor's threshold. Units: dimensionless · used on Risk · joint_vol_calibration/greeks/risk_monitor.py

The first use of each term on every page links here. A definition quotes the formula the code computes (the file named after it), not a textbook variant.