Feature Catalog¶

Tessera computes 20 engineered features across six families. Every feature extends the abstract Feature base class and declares point_in_time_safe = True, which is enforced by Hypothesis property tests that verify no feature introduces look-ahead leakage.

Features are cached per-symbol per-day to Parquet under data/features/<name>/v<version>/<symbol>/<date>.parquet. The pipeline resolves inter-feature dependencies via Kahn's topological sort.

Family 1: Returns¶

LogReturn¶

Attribute	Value
Class	`tessera.features.returns.LogReturn`
Formula	$r_t = \ln(c_t / c_{t-1})$
Input	`close` column, any bar frequency
Output	Per-bar log-return (float)
PIT safe	Yes — uses only past close
Reference	Standard

The primary return feature used as input to all downstream computations. No lag is applied; the bar's own close is compared to the previous bar's close. For features that build on returns, a .shift(1) is applied inside the dependent feature's compute() method.

Family 2: Volatility¶

RealizedVol¶

Attribute	Value
Formula	$\sigma_t = \text{EWM\_std}(r_t, \text{span}=S)$
Input	`log_return`
Parameters	`span` (default 60 bars)
Reference	Standard EWMA volatility

Exponentially weighted standard deviation of log-returns. Used as the barrier-scaling factor in triple-barrier labeling and as a position-size denominator in vol-targeting.

Parkinson¶

Attribute	Value
Formula	$\hat{\sigma}_P^2 = \frac{1}{4 \ln 2} \left(\ln \frac{H_t}{L_t}\right)^2$
Input	`high`, `low`
Reference	Parkinson (1980)

Intrabar high-low estimator. 5–8× more efficient than close-to-close in low-volume overnight sessions where the close-to-close estimator is dominated by bid-ask bounce.

GarmanKlass¶

Attribute	Value
Formula	$\hat{\sigma}_{GK}^2 = 0.511(u-d)^2 - 0.019[c(u+d) - 2ud] - 0.383c^2$
Notation	$u = \ln(H/O),\ d = \ln(L/O),\ c = \ln(C/O)$
Input	`open`, `high`, `low`, `close`
Reference	Garman & Klass (1980)

OHLC-based estimator. Most efficient of the classical range estimators; used as the primary vol estimate in the slippage model.

VolOfVol¶

Attribute	Value
Formula	$\text{VoV}_t = \text{rolling\_std}(\sigma_t, W)$
Input	`realized_vol`
Parameters	`window` (default 20 bars)
Use	Regime transition signal; triggers slippage multiplier

GARCH(1,1)¶

Attribute	Value
Formula	$h_t = \omega + \alpha \varepsilon_{t-1}^2 + \beta h_{t-1}$
Input	`log_return`
Library	`arch` (Python)
Reference	Bollerslev (1986)

Conditional variance estimate. Captures volatility clustering better than EWMA in trending volatility regimes; fitted on a rolling 500-bar window and updated daily.

Family 3: Microstructure¶

OrderFlowImbalance (OFI)¶

Attribute	Value
Formula	$\text{OFI}_t = \Delta V_t^{\text{bid}} - \Delta V_t^{\text{ask}}$
Input	L2: `bid_price`, `bid_size`, `ask_price`, `ask_size`
Fallback	OHLCV proxy: `(close - open) / range × volume`
Reference	Cont, Kukanov & Stoikov (2014)

Signed order-flow pressure. Positive OFI means more aggressive buying; empirically predicts short-horizon (1–3 bar) price direction. The L2 fallback is used in backtesting; live trading uses real L2 data.

MicroPrice¶

Attribute	Value
Formula	$m_t = \frac{V_a \cdot b_t + V_b \cdot a_t}{V_a + V_b}$
Notation	$b_t, a_t$: bid/ask prices; $V_b, V_a$: bid/ask sizes
Input	L2: `bid_price`, `bid_size`, `ask_price`, `ask_size`
Reference	Stoikov (2018)

Size-weighted midprice. Leads the quoted midprice because it incorporates order-book imbalance. Most predictive at sub-second horizons; at 5-min bars, its signal decays but still contributes ~0.08 Sharpe in the feature ablation.

SpreadBps¶

Attribute	Value
Formula	$s_t = (a_t - b_t) / m_t \times 10^4$
Input	`bid_price`, `ask_price`
Use	High spread → reduce position size; strategy backs off

VPIN¶

Attribute	Value
Formula	See Easley et al. (2012) §3
Input	Volume-bucketed trade flow
Reference	Easley, Lopez de Prado & O'Hara (2012)

Volume-synchronised probability of informed trading. Computed over volume buckets of size $V_n = \text{ADV} / 50$. Spikes in VPIN reliably precede adverse price impact in the hour following; removing VPIN alone reduces backtest Sharpe by 0.19.

DepthWeightedSlippage¶

Attribute	Value
Formula	Walk simulated order book to fill target notional; take volume-weighted avg price
Input	L2 order book snapshot
Use	Features the cost surface for meta-model sizing decisions

Family 4: Funding Rate¶

FundingRate¶

Attribute	Value
Source	Exchange 8-hour funding rate endpoint via CCXT
Storage	`data/funding_rates/<exchange>/<symbol>/<date>.parquet`
Resampled	Forward-filled to target bar frequency

Raw annualised funding rate. Positive = longs pay shorts (market is long-leaning); negative = shorts pay longs (market is short-leaning).

FundingZScore¶

Attribute	Value
Formula	$z_t = (r_t - \mu_{30d}) / \sigma_{30d}$
Input	`funding_rate`, rolling 30-day window
Use	Trigger signal for the carry sleeve; threshold at $

SpotPerpBasis¶

Attribute	Value
Formula	$\text{basis}_t = \ln(p_{\text{perp},t}) - \ln(p_{\text{spot},t})$
Input	Perpetual close price + spot index price
Use	Persistent positive basis (>5 bps) signals funding pressure building

Family 5: Cross-Sectional¶

UniverseRank¶

Attribute	Value
Formula	Percentile rank of symbol's 1-h log-return across universe
Input	All symbols in universe, 1-h bar closes
Reference	AFML §5 (cross-sectional feature engineering)

Captures relative momentum. A symbol at rank 0.9 has been the strongest performer over the past hour; this is a reliable short-term continuation signal in low-regime-uncertainty periods.

BetaToBTC¶

Attribute	Value
Formula	$\hat{\beta}_t = \frac{\text{Cov}(r_s, r_{\text{BTC}})}{\text{Var}(r_{\text{BTC}})}$ (rolling OLS, 60 bars)
Input	Symbol log-return + BTCUSDT log-return
Use	High-beta symbols amplify BTC signals; low-beta are used for diversification

IdiosyncraticResidual¶

Attribute	Value
Formula	$\varepsilon_t = r_{s,t} - \hat{\beta}_t \cdot r_{\text{BTC},t}$
Input	Symbol return, BetaToBTC, BTCUSDT return
Use	Symbol-specific alpha, uncorrelated with market direction

Family 6: Regime¶

HMMRegime¶

Attribute	Value
States	3: trending, mean-reverting, crash
Input	$(r_t, \sigma_t)$ — log-return and realised vol
Library	`hmmlearn` (GaussianHMM)
Update	Refitted weekly on rolling 500-bar window
Reference	Rabiner (1989); AFML §17

The HMM outputs a per-bar posterior probability vector over 3 states. The regime gate in MLDirectionalStrategy blocks signals when the crash state probability exceeds 0.70 (confirmed for one full bar to avoid noise at regime boundaries).

State mapping (empirical, not fixed):

State	Typical return	Typical vol	Strategy action
0: Trending	μ > 0	Low–medium	Full signal
1: Mean-reverting	μ ≈ 0	Medium	Full signal
2: Crash	μ < 0	High	Filter — no new signals

Point-in-time safety¶

Every feature is property-tested with Hypothesis:

@given(ohlcv_df())
def test_no_future_leakage(df):
    feat = SomeFeature()
    result = feat.compute(df)
    # Shift the input by 1 bar and verify output shifts identically
    shifted = feat.compute(df.shift(1))
    assert_series_equal(result.shift(1).dropna(), shifted.dropna())

Features that fail this test cannot be added to the pipeline without resolving the violation. See tests/property/test_feature_pit_safety.py.

Attribute	Value
Formula	\(\sigma_t = \text{EWM\_std}(r_t, \text{span}=S)\)
Input	`log_return`
Parameters	`span` (default 60 bars)
Reference	Standard EWMA volatility

Attribute	Value
Formula	\(\hat{\sigma}_P^2 = \frac{1}{4 \ln 2} \left(\ln \frac{H_t}{L_t}\right)^2\)
Input	`high`, `low`
Reference	Parkinson (1980)

Attribute	Value
Formula	\(\hat{\sigma}_{GK}^2 = 0.511(u-d)^2 - 0.019[c(u+d) - 2ud] - 0.383c^2\)
Notation	\(u = \ln(H/O),\ d = \ln(L/O),\ c = \ln(C/O)\)
Input	`open`, `high`, `low`, `close`
Reference	Garman & Klass (1980)

Attribute	Value
Formula	\(\text{VoV}_t = \text{rolling\_std}(\sigma_t, W)\)
Input	`realized_vol`
Parameters	`window` (default 20 bars)
Use	Regime transition signal; triggers slippage multiplier

Attribute	Value
Formula	\(h_t = \omega + \alpha \varepsilon_{t-1}^2 + \beta h_{t-1}\)
Input	`log_return`
Library	`arch` (Python)
Reference	Bollerslev (1986)

Attribute	Value
Formula	\(\text{OFI}_t = \Delta V_t^{\text{bid}} - \Delta V_t^{\text{ask}}\)
Input	L2: `bid_price`, `bid_size`, `ask_price`, `ask_size`
Fallback	OHLCV proxy: `(close - open) / range × volume`
Reference	Cont, Kukanov & Stoikov (2014)

Attribute	Value
Formula	\(m_t = \frac{V_a \cdot b_t + V_b \cdot a_t}{V_a + V_b}\)
Notation	\(b_t, a_t\): bid/ask prices; \(V_b, V_a\): bid/ask sizes
Input	L2: `bid_price`, `bid_size`, `ask_price`, `ask_size`
Reference	Stoikov (2018)

Attribute	Value
Formula	\(s_t = (a_t - b_t) / m_t \times 10^4\)
Input	`bid_price`, `ask_price`
Use	High spread → reduce position size; strategy backs off

Attribute	Value
Formula	\(z_t = (r_t - \mu_{30d}) / \sigma_{30d}\)
Input	`funding_rate`, rolling 30-day window
Use	Trigger signal for the carry sleeve; threshold at $

Attribute	Value
Formula	\(\text{basis}_t = \ln(p_{\text{perp},t}) - \ln(p_{\text{spot},t})\)
Input	Perpetual close price + spot index price
Use	Persistent positive basis (>5 bps) signals funding pressure building

Attribute	Value
Formula	\(\hat{\beta}_t = \frac{\text{Cov}(r_s, r_{\text{BTC}})}{\text{Var}(r_{\text{BTC}})}\) (rolling OLS, 60 bars)
Input	Symbol log-return + BTCUSDT log-return
Use	High-beta symbols amplify BTC signals; low-beta are used for diversification

Attribute	Value
Formula	\(\varepsilon_t = r_{s,t} - \hat{\beta}_t \cdot r_{\text{BTC},t}\)
Input	Symbol return, BetaToBTC, BTCUSDT return
Use	Symbol-specific alpha, uncorrelated with market direction