Appearance
Analytics catalogue
Kairos ships 139 analytics across six families. Every analytic obeys the same contracts: replay parity, deterministic single-consumer ordering, fail-closed trust-boundary validation, no allocations on the per-tick hot path in steady state, and the suppress-when-undefined emission contract.
Each analytic page carries its methodology citation, the generated spec and tick field tables, and Python / TypeScript / Rust examples. Drive availability is shown per analytic: live, historical, and replay. Cache-dependent analytics fail closed on the historical drive with KAIROS_ERR_HISTORICAL_UNWIRED until the relevant cache is hydrated externally.
| Family | Count | Scope |
|---|---|---|
| Flow surveillance | 43 | Order-flow, dealer-positioning, and breadth aggregators |
| Volatility | 36 | Implied and realized volatility |
| Microstructure | 27 | Liquidity and price-impact diagnostics |
| Risk | 14 | Tail-risk and drawdown |
| Stat-arb | 16 | Cross-sectional and no-arbitrage residuals |
| Data primitives | 3 | Foundational tick shapes |
Flow surveillance
Order-flow, dealer-positioning, and breadth aggregators — from per-print aggressor classification to universe-wide market-tide and McClellan breadth.
| Analytic | Methodology | Modes |
|---|---|---|
| Aggressor Intensity | Lee-Ready (1991) aggressor-rate streaming aggregator; buyer / seller / total classified rate over a rolling time window | live / historical / replay |
| Aggressor Sign | Lee-Ready tick rule | live / historical / replay |
| Arms Index TRIN | Arms (1967) Trading Index (advances / declines) / (up_volume / down_volume) across the matched-cohort universe | live / historical / replay |
| Block Trade | premium-tier threshold | live / historical / replay |
| CEX | dealer charm-exposure aggregator: Sum ±charm_i × OI_i × multiplier × spot across chain — intraday time-decay-of-del… | live / historical / replay |
| Closing Auction Imbalance | Lee-Ready (1991) signed-volume imbalance over the pre-close auction window | live / historical / replay |
| DEX | dealer delta-exposure aggregator: Sum ±Δ_i × OI_i × multiplier × spot across chain | live / historical / replay |
| Option Trades | Lee-Ready (1991) aggressor sign | live / historical / replay |
| Flow Recap | session aggregator | live / historical / replay |
| Flow Summary | Bloomberg OMON per-root rollup; sweep (multi-venue cluster) + block (size) classification | live / historical / replay |
| Gamma Squeeze Risk | call-OI / float × short-interest composite | live / historical / replay |
| GEX | dealer gamma exposure (per-strike) | live / historical / replay |
| GEX Levels | per-strike GEX clustering ranked by ` | chain + OI + spot |
| Greek Flow | per-symbol multi-Greek trade-flow aggregator: Sum_trades (greek · signed_qty) across (delta, gamma, vega, theta) ov… | live / historical / replay |
| Halt Event | LULD / regulatory halt detector | live / historical / replay |
| Large Print Percentile | Jain / Chlamtac (1985) P² streaming-quantile block detector; fires per-event when admitted print size crosses the r… | live / historical / replay |
| Market Breadth | universe-wide premium-weighted P/C ratio + net-delta proxy + advancing / declining (OMON Composite) | live / historical / replay |
| Market Thrust | Zweig (1986) streaming EMA over the universe advance ratio at the 10-period anchor; (0.40 → 0.615) threshold-cross… | live / historical / replay |
| Market Tide | universe-wide aggregate tape-aggregator (SpotGamma Market Tide, FlowAlgo Tape, CBOE OMON Composite) | live / historical / replay |
| Max Pain | per-strike `OI × | chain + OI |
| Mcclellan Oscillator | McClellan (1969) universe-wide dual 19 / 39-period EMA of the advances − declines spread; NYSE breadth-momentum osc… | live / historical / replay |
| Multi Leg Detector | synchronized-fill structure detection | live / historical / replay |
| Net Premium | per-root running net-premium odometer with Lee-Ready (1991) aggressor classification per print | live / historical / replay |
| OI Changes | per-contract day-over-day open-interest delta oi_today - oi_prev — Kolanovic (2014) / SqueezeMetrics (2017) accumul… | live / replay (historical cache-gated) |
| OI Heatmap | per-(expiration, strike) open-interest grid recovered off the chain snapshot + open-interest cache pair — the Squee… | live / replay (historical cache-gated) |
| Open Interest | per-contract OI stream | live / historical |
| Opening Auction Imbalance | Lee-Ready (1991) signed-volume imbalance (buy_volume − sell_volume) / total_volume over the post-open auction window | live / historical / replay |
| Opex Pinning | Gaussian-weighted GEX concentration | live / historical / replay |
| Option Flow | premium-weighted aggregator | live / historical / replay |
| P/C OI Ratio | chain-level put / call open-interest ratio sum oi_put / sum oi_call plus signed-imbalance twin — CBOE put / call ra… | live / replay (historical cache-gated) |
| P/C Volume Ratio | rolling-window put / call volume ratio over sliding intraday FIFO of admitted option trades — CBOE put / call ratio m… | live / historical / replay |
| Put Call Ratio | premium-weighted P/C | live / historical / replay |
| Relative Volume | Bloomberg VOLA per-root current-session volume vs trailing-N baseline | live / replay (historical cache-gated) |
| Sector Rotation Strength | per-cadence per-sector mean-return ladder under the desk-supplied symbol → sector taxonomy mapping (Bloomberg `MOST R… | live / historical / replay |
| Institutional Flow Score | 6-component composite (premium / spread / aggressor / OI / venue / DTE) | live / historical / replay |
| Stock Flow | underlying tape aggregator | live / historical / replay |
| Sweep Clustering | rolling-window aggregator over Lee-Ready (1991) same-side print-burst clusters; companion to sweep_detector | live / historical / replay |
| Sweep Detector | Reg NMS Rule 611 multi-venue, Hendershott (2013) | live / historical / replay |
| Technical Indicators | RSI / MACD / Bollinger bundle | live / historical / replay |
| Tick Index | NYSE TICK-style universe-wide signed-tick aggregator over per-symbol Lee-Ready (1991) last-tick directions | live / historical / replay |
| Volume Anomaly | rolling z-score vs N-session baseline | live / historical / replay |
| VEX | dealer vega-exposure aggregator: Sum ±ν_i × OI_i × multiplier across chain | live / historical / replay |
| Volume Profile | per-price-bucket volume distribution with Point of Control + Dalton-Jones-Dalton (1990) value-area envelope per Steid… | live / historical / replay |
Volatility
Implied and realized volatility — Black–Scholes Greeks, CBOE-method surfaces, GARCH and HAR forecasts, jump tests, and the OHLC realized-vol estimator family.
| Analytic | Methodology | Modes |
|---|---|---|
| Bipower Variation | Barndorff-Nielsen / Shephard (2004) jump-robust bipower variation `BPV = (π / 2) · Σ | r_ |
| Calendar Spread Edge | Natenberg (2015) §18 closed-form V_theo ≈ K · σ · sqrt(Δτ) / sqrt(2π) | live / historical / replay |
| Expected Move | Black-Scholes (1973) one-sigma expected move EM = spot * sigma * sqrt(T) at the ATM strike via Brenner-Subrahmanyam… | live / replay (historical cache-gated) |
| Forward Variance | Demeterfi-Derman-Kamal-Zou (1999) VIX-style forward variance swap rate (T2*σ²(T2) - T1*σ²(T1)) / (T2-T1) over Carr-… | live / replay (historical cache-gated) |
| Garch Forecast | Engle (1982) GARCH(1,1), Hansen-Lunde (2005) loadings α=0.10 / β=0.85 | live / replay (historical cache-gated) |
| Garch Proxy | Bollerslev (1986) intraday GARCH(1,1) streaming conditional-volatility recursion `σ²_t = ω + α · r²_{t-1} + β · σ²_{t… | live / historical / replay |
| Garman Klass Explicit | Garman / Klass (1980) OHLC realized volatility σ²_GK = 0.5 · ln(H/L)² − (2·ln 2 − 1) · ln(C/O)² aggregated over a r… | live / historical / replay |
| Greeks | Black-Scholes-Merton + dividend yield | live / historical / replay |
| HAR RV | Corsi (2009) Heterogeneous Autoregressive realized-volatility forecast `RV̂_{t+1} = β₀ + β_d · RV_{d,t} + β_w · RV_{w… | live / historical / replay |
| Historical Vol | Parkinson / Garman-Klass / close-close | live / replay (historical cache-gated) |
| IV Band 52-week | 52-week IV percentile rank per tenor | live / replay (historical cache-gated) |
| IV Change | first-derivative IV stream | live / historical / replay |
| IV Cone | percentile rank per lookback {252,60,20,5} | live / replay (historical cache-gated) |
| IV Rank | tastytrade / Bloomberg IMP_VOL_RANK normalization (IV_now - IV_min_252) / (IV_max_252 - IV_min_252) on the traili… | live / replay (historical cache-gated) |
| IV Skew | 25-delta risk reversal + butterfly | live / historical / replay |
| IV Summary | Brenner-Subrahmanyam (1988) straddle-implied ATM IV per listed expiration `sigma_atm = sqrt(2*pi/T) * (C_atm + P_atm)… | live / replay (historical cache-gated) |
| IV Term Structure | fixed-slot tenor ladder (30/60/90/120/180/360/720d) | live / historical / replay |
| Jump Test | Barndorff-Nielsen / Shephard (2004) RV/BV, Huang-Tauchen (2005) finite-sample guard | live / historical / replay |
| Lee Mykland Jumps | Lee / Mykland (2008) high-frequency per-bar jump detector — standardizes each sealed return against the bipower-deriv… | r_ |
| MedRV | Andersen / Dobrev / Schaumburg (2012) median realized variance with c_med = π / (6 − 4·√3 + π) | live / historical / replay |
| Parkinson Explicit | Parkinson (1980) high-low realized volatility σ²_P = ln(H/L)² / (4 · ln 2) aggregated over a rolling per-bar `(H, L… | live / historical / replay |
| Price Band 52-week | 52-week range tracker | live / replay (historical cache-gated) |
| Realized Semi Variance | Barndorff-Nielsen / Kinnebrock / Shephard (2010) RV⁺ / RV⁻ decomposition, Patton-Sheppard (2015) signed asymmetry | live / historical / replay |
| Realized Vol Cone | RV percentile cone at {1,5,10,20,60}d | live / replay (historical cache-gated) |
| Risk Neutral Density | Breeden-Litzenberger (1978) q(K) = e^{rT} * d²C/dK² density via the three-point non-uniform-grid stencil on the lis… | live / replay (historical cache-gated) |
| Risk Reversal Velocity | d(RR25)/dt annualized (5.9M sec/yr) | live / historical / replay |
| Rogers Satchell Vol | Rogers / Satchell (1991) drift-independent OHLC variance kernel σ²_RS = ln(H/C) · ln(H/O) + ln(L/C) · ln(L/O) aggre… | live / historical / replay |
| Smile Dynamics | Derman (1999) regime classifier | live / historical / replay |
| Vanna Charm Flow | Hull (2018) §19.7 vanna + charm closed-form proxies; per-symbol rolling-window aggregator over option prints | live / historical / replay |
| Variance Swap Quote | Carr-Madan (1998) model-free variance | live / historical / replay |
| Vix Synthetic | Demeterfi-Derman-Kamal-Zou (1999) 30-day synthetic VIX over the bracketing-expiration OTM chain time-interpolated to… | live / replay (historical cache-gated) |
| Vol Moments | Bakshi-Kapadia-Madan (2003) model-free risk-neutral skew + kurtosis via cubic + quartic static-replication integrals | live / replay (historical cache-gated) |
| Vol Risk Premium | Bollerslev / Tauchen / Zhou (2009) per-symbol streaming spread vrp = implied_vol - realized_vol; realized vol via P… | live / historical / replay |
| Vol Surface Factors | Carr-Wu (2009) / Gatheral-Jacquier (2014) SVI / SSVI per-tenor level / slope / curvature OLS fit on log-moneyness | live / replay (historical cache-gated) |
| Volatility | CBOE VIX methodology + CUSUM + EWMA filter | live / historical / replay |
| Yang Zhang Vol | Yang / Zhang (2000) minimum-variance OHLC composite σ²_YZ = σ²_overnight + k · σ²_oc + (1 − k) · σ²_RS with the Yan… | live / historical / replay |
Microstructure
Liquidity and price-impact diagnostics — VPIN toxicity, Kyle's lambda, order-flow imbalance, spread decomposition, and quote-quality gauges.
| Analytic | Methodology | Modes |
|---|---|---|
| Amihud Illiquidity | Amihud (2002) illiquidity ratio `ILLIQ = (1/T) · Σ | daily-close cache |
| Bid Ask Persistence | Bayer / Liesenfeld (2010) Bayesian Beta-Bernoulli posterior change-probability of the NBBO mid-quote over a rolling N… | live / historical / replay |
| Book Depth At Top | Foucault / Pagano / Röell (2013) §5 total displayed top-of-book size bid_size + ask_size aggregated over admitted N… | live / historical / replay |
| CVD | cumulative volume delta + Lee-Ready | live / historical / replay |
| Depth Imbalance | Stoikov (2018) signed NBBO depth-skew ratio (bid_size − ask_size) / (bid_size + ask_size) in [-1, +1] — top-of-bo… | live / historical / replay |
| Effective Spread | Bessembinder (2003) effective half-spread `ES_t = 2· | trade + quote tape |
| Hasbrouck Info Share | per-venue return-variance share (Hasbrouck 1995 price-discovery tradition; loading-aware information share is the des… | live / historical / replay |
| Hawkes Intensity | Hawkes (1971) self-exciting intensity via the rate-invariant inter-arrival CV² branching proxy; Bacry-Mastromatteo-Mu… | live / historical / replay |
| Huang Stoll Lambda | Huang / Stoll (1997) two-way decomposition — permanent (information-driven) price-impact slope λ + realized half-sp… | live / historical / replay |
| Kyles Lambda | Kyle (1985) OLS price-impact regression | live / historical / replay |
| Microprice | Gatheral-Oomen (2010) depth-weighted mid microprice = (bid · ask_size + ask · bid_size) / (bid_size + ask_size) — s… | live / historical / replay |
| Mid Info Share | Madhavan-Richardson-Roomans (1997) two-coefficient OLS on tick-rule sign, info_share = 100·θ²/(θ²+φ²) | live / historical / replay |
| Odd Lot Ratio | O'Hara / Yao / Ye (2014) §IV odd-lot fraction oddlot_count / total_count over a rolling window — informed-retail or… | live / historical / replay |
| OFI | Cont-Kukanov-Stoikov (2014) NBBO-event imbalance | live / historical / replay |
| PIN Classic | Easley-López de Prado-O'Hara (2012) moment-proxy estimator PIN = μ̂/(μ̂ + 2ε̂) (EKOP 1996 tradition) | live / historical / replay |
| Price Dispersion | within-window dimensionless std(prices) / mean(prices) liquidity-stratification proxy | live / historical / replay |
| Queue Imbalance | Cartea / Donnelly / Jaimungal (2015) signed NBBO depth pressure (bid_size − ask_size) / (bid_size + ask_size) in `[… | live / historical / replay |
| Quote Intensity | Hendershott / Riordan (2013) §III.B HFT-activity proxy — admitted quote / trade event-rate over a rolling window with… | live / historical / replay |
| Quote Lifetime | Per-side log10-spaced NBBO sealed-lifetime histogram across the bid and ask legs over the active session — per-leg de… | live / historical / replay |
| Realized Spread | Huang / Stoll (1996) realized half-spread RS_t = 2·D_t·(P_t − M_{t+τ}) / M_t post-trade decay aggregated over a rol… | live / historical / replay |
| Rolls Measure | Roll (1984) implicit spread s = 2·sqrt(−cov(Δp_t, Δp_{t-1})) | live / historical / replay |
| Spread Efficiency | Roll (1984) inspired E[(Δp)²] / E[spread²] tradability proxy over a rolling window | live / historical / replay |
| Tick Rule Imbalance | Easley / O'Hara (1987) tick-rule signed-volume imbalance (uptick_volume − downtick_volume) / total_volume over a ro… | live / historical / replay |
| Top Book Persistence | Hasbrouck-Saar (2013) running mean lifetime of the NBBO inside between consecutive L1 changes via Welford (1962) runn… | live / historical / replay |
| Variance Ratio Test | Lo / MacKinlay (1988) random-walk test VR(q) = Var(r_q) / (q · Var(r_1)) with the overlapping-sample null variance… | live / historical / replay |
| VPIN | López de Prado (2012) volume-synchronized PIN | live / historical / replay |
| VWAP TWAP deviation | Welford weighted recurrence (West 1979) + NaN warmup | live / historical / replay |
Risk
Tail-risk and drawdown — historical and parametric VaR / CVaR, SPAN margin, circuit-breaker proximity, and the drawdown-penalty ratios.
| Analytic | Methodology | Modes |
|---|---|---|
| Circuit Breaker Proximity | NYSE Rule 7.12 / Cboe Rule 6.32 thresholds (-7% / -13% / -20%) | live / replay (historical cache-gated) |
| Conditional VaR | Rockafellar / Uryasev (2000) discrete Expected Shortfall CVaR = VaR + (1/(pN)) · Σ(Q_p − r)⁺ over the exact rolling… | live / historical / replay |
| LULD Proximity | SEC NMS LULD Plan + last-25-min band doubling | live / historical / replay |
| Max Drawdown Stream | Magdon-Ismail / Atiya (2004) rolling peak-to-trough maximum drawdown MDD = max((peak − trough) / peak); the Calmar-… | live / historical / replay |
| Omega Ratio | Keating / Shadwick (2002) probability-weighted gain / loss ratio Ω(τ) = E[max(r − τ, 0)] / E[max(τ − r, 0)] over ro… | live / historical / replay |
| Pain Index | Becker (2006) arithmetic-mean drawdown `PI = mean( | stock trade tape (5m bars) |
| Portfolio VaR | RiskMetrics historical-simulation VaR + Acerbi-Tasche ES | live / replay (historical cache-gated) |
| Return Kurtosis | Welford (1962) standardised fourth central moment (excess kurtosis) of per-bar log returns K = m_4 / m_2² − 3 over… | live / historical / replay |
| Return Skewness | Welford (1962) standardised third central moment of per-bar log returns S = m_3 / m_2^{3/2} over a rolling window —… | live / historical / replay |
| Sortino Ratio | Sortino / Price (1994) downside-deviation risk-adjusted return (R̄ − MAR) / sqrt(mean(min(r − MAR, 0)²)); per-bar p… | live / historical / replay |
| SPAN Margin | OCC SPAN 16-scenario grid | live / historical / replay |
| Ulcer Index | Martin (1989) drawdown-depth-and-duration penalty UI = sqrt(mean(DD_i²)) over rolling window per-bar close FIFO | live / historical / replay |
| VaR Historical | exact Hyndman-Fan Type 7 lower-tail order statistic over the rolling per-bar return window; the unbounded session-anc… | live / historical / replay |
| VaR Parametric | J.P. Morgan RiskMetrics (1996) Gaussian-assumption parametric VaR VaR_α = −(μ + z_α · σ) over a rolling per-bar ret… | live / historical / replay |
Stat-arb
Cross-sectional and no-arbitrage residuals — pairs cointegration, put-call parity and box-spread residuals, and the convexity / monotonicity screens.
| Analytic | Methodology | Modes |
|---|---|---|
| Beta To SPY | Sharpe (1964) OLS regression vs SPY | live / replay (historical cache-gated) |
| Box Spread | 4-leg synthetic funding rate (Boyarchenko / Eisenbach) | live / historical / replay |
| Box Spread Arb Residual | Stoll (1969) / Hull (2018) four-leg European box-spread residual `(C(K1) − P(K1)) − (C(K2) − P(K2)) − (K2 − K1) · e^{… | live / replay (historical cache-gated) |
| Butterfly Arb Residual | Carr-Madan (2001) discrete butterfly no-arbitrage residual C(K-h) − 2·C(K) + C(K+h) at every interior strike on the… | live / replay (historical cache-gated) |
| Calendar Arb Residual | Merton (1973) Theorem 5 calendar-spread time-monotonicity residual C(K, T_far) − C(K, T_near) at every shared strik… | live / replay (historical cache-gated) |
| Conversion Arb | C − P − S + (K + D) · e^(−rT) edge detector | live / historical / replay |
| Engle Granger Residual | Engle-Granger (1987) Stage-1 long-run OLS residual stream ε_t = log(price_a) − γ̂ − δ̂ · log(price_b) with per-tick… | live / replay (historical cache-gated) |
| Half Life OU | Ornstein-Uhlenbeck mean-reversion half-life t₁/₂ = -ln(2) / ln(φ̂) via Yule-Walker (1927) AR(1) on rolling per-bar… | live / historical / replay |
| Hurst Exponent | Mandelbrot-Wallis (1969) rescaled-range R/S with the Anis-Lloyd (1976) centered estimator `H = ½ + (ln(R/S) − ln E₀[R… | live / historical / replay |
| Implied Dividend | parity-implied PV(div) | live / historical / replay |
| Implied Spot | put-call parity inversion | live / historical / replay |
| Pairs Cointegration | Engle-Granger (1987) 2-step + MacKinnon (1991) ADF critical value −3.34 | live / replay (historical cache-gated) |
| Put Call Parity Residual | Stoll (1969) / Black-Scholes-Merton (1973) European put-call parity residual C − P − (S − K · e^{-rT}) at every sha… | live / replay (historical cache-gated) |
| Rolling Beta | Sharpe (1964) rolling-OLS market-model beta vs subscriber-supplied benchmark — Fama-MacBeth (1973) rolling-window con… | live / replay (historical cache-gated) |
| Rolling Correlation | Pearson (1895) product-moment correlation ρ ∈ [-1, +1] over trailing daily log-return window — Gatev / Goetzmann /… | live / replay (historical cache-gated) |
| Vertical Arb Residual | Merton (1973) Theorem 2 vertical-spread monotonicity residual C(K_low) − C(K_high) at every adjacent strike pair on… | live / replay (historical cache-gated) |
Data primitives
Foundational tick shapes — OHLCVC bars, per-contract moneyness slices, and bid-ask spread events.
| Analytic | Methodology | Modes |
|---|---|---|
| OHLCVC | OHLC + volume + count per time bucket | live / historical / replay |
| Per Contract Moneyness Slice | per-contract moneyness snapshot | live / historical / replay |
| Spread Detector | bid-ask spread anomaly | live / historical / replay |
Field-level glossary
Each analytic page documents its emitted Tick schema and its *Params configuration struct inline — both regenerated from the Rust source on every build. See tick types for the shared tick-contract conventions and universe selection for the symbol-first accessor argument and the for_index / for_sector selectors every analytic shares.