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Quantitative model catalog

This catalog distinguishes implemented research baselines from models that remain outside version 0.2.0.

Stochastic processes

Model Dispatcher key Main parameters Numerical method
Arithmetic Brownian motion abm drift, normal volatility Gaussian increments
Geometric Brownian motion gbm drift, lognormal volatility exact log transition
Correlated GBM lower-level function vectors + correlation Cholesky Gaussian shocks
Ornstein-Uhlenbeck ou speed, long mean, volatility Euler
CIR cir speed, long mean, volatility full-truncation Euler
Vasicek vasicek speed, long mean, volatility exact Gaussian transition
Heston heston variance mean reversion, vol-of-vol, correlation full-truncation Euler
Merton jump diffusion merton diffusion + Poisson-normal jumps time discretization

All stochastic APIs expose seeds and return SimulationResult, including full paths, terminal values, parameter metadata, summary statistics, and plotting shortcuts.

Monte Carlo

monte_carlo_price(...) accepts a simulation and an arbitrary terminal payoff. Specialized wrappers implement:

  • European calls and puts under risk-neutral GBM;
  • arithmetic-average Asian calls and puts;
  • antithetic sampling for GBM;
  • standard error and normal-approximation confidence interval.

Monte Carlo confidence intervals quantify simulation error under the sampled model. They do not include parameter uncertainty or model risk.

Derivative pricing

Model Scope
Black-Scholes-Merton European equity-style calls/puts with continuous dividend yield and analytic Greeks
Bachelier European normal-model calls/puts with forward, normal volatility, and discounting
Black-76 European options on forwards/futures
CRR binomial European and American calls/puts
Monte Carlo GBM European and arithmetic-average Asian calls/puts

The unified entry point is price_option(model, ...) or lab.option(model, ...).

Martingale diagnostics

martingale_diagnostics(...) evaluates selected finite-sample implications of a discounted martingale:

  • zero unconditional mean of increments;
  • no linear predictability from the lagged level under HAC covariance;
  • no increment autocorrelation at a selected Ljung-Box horizon.

Non-rejection is not proof of the conditional-expectation definition.

Regression and time series

Implemented families:

  • OLS with classical, HC0-HC3, or Newey-West/HAC covariance;
  • rolling OLS;
  • quantile regression;
  • polynomial regression;
  • Ridge, Lasso, and Elastic Net;
  • logistic regression;
  • factor regression;
  • ADF and KPSS stationarity tests;
  • Engle-Granger cointegration test;
  • Granger-predictive tests;
  • ARIMA and VAR;
  • moving-block bootstrap, permutation testing, and Benjamini-Hochberg FDR.

Regression outputs retain aligned fitted values, residuals, confidence intervals, and diagnostics. Statistical significance is not causal identification.

Machine learning

The package provides:

  • explicit lag features;
  • technical features based only on current and past prices;
  • forward return or direction targets;
  • chronological walk-forward fitting;
  • expanding or rolling training windows;
  • an explicit train-test gap;
  • regression and classification metrics;
  • fitted models and out-of-sample prediction paths.

The user supplies any scikit-learn-compatible estimator. ASRQuant does not claim that a model is economically useful merely because predictive metrics are positive.

Portfolio and covariance models

Covariance estimators:

  • sample;
  • exponentially weighted;
  • Ledoit-Wolf;
  • Oracle Approximating Shrinkage.

Allocators:

  • minimum variance;
  • maximum Sharpe;
  • equal-risk contribution;
  • maximum diversification;
  • hierarchical risk parity;
  • Black-Litterman posterior construction;
  • random efficient-frontier analysis.

Volatility

  • rolling realized volatility;
  • Parkinson range estimator;
  • Garman-Klass OHLC estimator;
  • EWMA volatility;
  • optional GARCH forecast through the arch extra.

Fixed income

  • zero-coupon pricing;
  • fixed-rate bond cash flows and pricing;
  • yield to maturity;
  • Macaulay and modified duration;
  • convexity;
  • simple par-instrument zero-curve bootstrapping.

Not implemented in 0.2.0

Specialist extensions still include local volatility, SABR, Hull-White, affine multi-factor term structures, credit intensity, exotics, adjoint differentiation, calibration frameworks, order-book simulation, event-driven execution, and production broker connectivity.

Universal Monte Carlo estimators (1.0.0)

The universal engine separates scenario generation, pathwise quantity evaluation and statistical reduction. Built-in reductions are expectation, probability, variance, standard deviation, median, quantile, VaR, Expected Shortfall, minimum and maximum. A custom callable may be used as the reducer.

Scenario utilities include inverse-transform sampling, Gaussian generation, Cholesky-correlated Gaussian vectors and generic Euler-Maruyama dynamics. Pathwise hedging losses include proportional transaction costs.

Approximation and response surfaces (1.0.0)

  • piecewise-linear interpolation;
  • bilinear interpolation on regular grids;
  • cubic splines;
  • Gaussian Nadaraya-Watson kernel regression;
  • radial-basis interpolation;
  • Gaussian-process regression with predictive uncertainty;
  • linear, polynomial, ridge and lasso response regressions;
  • controlled extrapolation;
  • RMSE, MAE and R-squared validation;
  • first- and second-order surface sensitivities.