Kalman Filter
Linear-Gaussian state-space estimator; used for token-level price/velocity tracking.
Quant
The mathematics I actually ship — filters, factor research, volatility models, options pricers, risk metrics, microstructure. Implemented in Rust and Python across kokoro-alpha-lab and kokoro-pricing-service.
Filters & State Estimation
Unscented Kalman Filter
Sigma-point nonlinear filtering with automatic warm-up for non-Gaussian dynamics.
Particle Filter
Sequential importance resampling with distribution snapshots for multimodal posteriors.
H-infinity Filter
Robust state-space filter with measurement gating and velocity inflation under adversarial noise.
Conformal Prediction
Distribution-free calibrated prediction intervals around any point forecaster.
Signal Processing
Fourier Analysis
Frequency-domain decomposition for cycle detection and harmonic extraction.
Continuous Wavelet Transform
Multi-scale time-frequency decomposition with regime-change detection.
Hilbert Transform
Analytic signal yielding instantaneous phase and frequency.
L1 Trend Filtering
Nonparametric trend isolation via L1-penalised smoothing.
Volatility & Time-Series
GARCH(1,1)
Conditional variance forecasting with grid-search fit and variance targeting.
EWMA (RiskMetrics λ=0.94)
Exponentially-weighted variance estimator for short-horizon vol.
Bipower Variation
Barndorff-Nielsen & Shephard decomposition isolating jumps from realised variance.
Hurst Exponent (R/S)
Multi-scale rescaled-range analysis distinguishing trend persistence from mean reversion.
Augmented Dickey-Fuller
OLS-based stationarity test with MacKinnon critical values.
Risk Metrics
Parametric & Historical VaR
Quantile loss estimators from both fitted normals and empirical distributions.
Conditional VaR (Expected Shortfall)
Tail-mean loss beyond the VaR threshold.
Maximum Drawdown
Peak-to-trough underwater analysis on equity curves.
Annualised Sharpe
Risk-adjusted return with √252 scaling; the standard hurdle metric.
Greeks-Based Portfolio Risk
Aggregated Δ / Γ / Vega for options inventory.
Options & Derivatives
Black-Scholes
Closed-form European pricer plus analytical Δ / Γ / Θ / Vega / ρ.
Newton-Raphson IV Solver
Implied-volatility extraction via gradient descent on Vega.
Cox-Ross-Rubinstein Tree
Discrete binomial pricer with backward induction for American features.
Monte Carlo Pricer
GBM path simulation with Box-Muller draws and confidence intervals.
Portfolio Optimisation
Markowitz Mean-Variance
Unconstrained (analytical) and constrained (projected gradient / SLSQP) weight allocation.
Efficient Frontier
Risk-return locus swept across the target-return space.
Kelly Criterion
Log-optimal bet sizing for repeated edges.
Market Microstructure
Order Flow Imbalance
L2-based ΔBid − ΔAsk with level-improvement logic; classified into directional pressure.
VWAP & Median Aggregation
Volume-weighted and outlier-robust price blends across DEX sources.
Slippage Curves
Depth-profiled execution cost from quote-API ladder sweeps.
Hawkes Self-Exciting Process
Baseline / excitation / decay cascade model for event clustering.
Stochastic Methods
Gaussian & Student-t Copulas
Cholesky-sampled dependence with heavy-tailed variants for joint scenarios.
Importance Sampling
Biased-distribution reweighting for rare-event variance reduction.
Antithetic & Control Variates
Negatively-correlated path pairing and proxy-variable correction.
Stratified Sampling
Uniform bucket coverage for Monte Carlo integrators.
Statistical Learning
K-Means + Silhouette
Euclidean clustering with cohesion / separation quality scoring.
Mahalanobis Distance
Covariance-weighted distance for anomaly and regime discrimination.
Mechanism Design
LMSR
Logarithmic Market Scoring Rule — the cost-function AMM for prediction markets.
Alpha Factor Library
Twenty-four distinct factors, each its own crate with bespoke calibration — not re-skinned momentum.
Swap MomentumPrice TrendOrder FlowRegime DetectionCluster ActivityDepth QualityWhale FlowSmart MoneyAMM StateHierarchical FilterConsensusHawkes CascadeAI EnsembleSocial SentimentEquity MomentumEquity Mean-ReversionPairs / CointegrationSector RotationForex CarryOptions Vol SurfaceOptions SkewGamma ScalpingCalendar SpreadComposer Roles
Numerical Methods
- Newton-Raphson for implied vol and root finding
- Projected gradient descent for constrained mean-variance
- SLSQP (Python / SciPy) for equality- and inequality-constrained portfolios
- Box-Muller normal-deviate generation for path simulators
- Cholesky decomposition for correlated copula sampling
- OLS closed-form regression for slope / intercept estimators