Knowledge library

This case study fits regularized linear models to returns from short at-the-money straddles held to expiry. Because premium income caps the gain while losses can grow without bound, a few severe losses dominate a squared-error regression objective. The…

This notebook constructs four model-based features for S&P 500 option research: next-day volatility forecasts from GJR-GARCH and stochastic volatility, plus the differences between each forecast and the option market’s implied volatility. It explains how the…

This notebook tests whether learned graph embeddings add predictive information to a tabular model for US stocks. It builds a network from absolute return correlations measured before the target period, constructs momentum, volatility, and trend features…

This notebook compares ways to measure volatility and develops heterogeneous autoregressive (HAR) volatility models alongside roughness analysis. It uses intraday returns to estimate session realized variance, distinguishes intraday movement from overnight…

This notebook compares four reference ETF allocations using historical crisis windows, hand-authored simultaneous asset shocks, Student-t Monte Carlo simulations, and market-regime statistics. It explains a maximum drawdown measure and uses daily…

This notebook diagnoses how a fixed, long-only ETF momentum baseline performed across market conditions from 2010 to 2024. It labels each daily return using volatility and trend measures known before that return began, with expanding historical medians…

This notebook develops Black-Scholes pricing for European calls and puts, checks put-call parity, and computes implied volatility with Brent root-finding. It also defines Delta, Gamma, Vega, Theta, and Rho and uses plots to illustrate how option…

This ETF feature notebook explains how fitted statistical models can leak future information through their estimated parameters, even when their formulas use past observations. Its remedy is a walk-forward refit schedule: allow an initial burn-in, fit using…

This case study constructs features for comparing variance risk premiums across S&P 500 stocks using 30-day at-the-money straddles and underlying price data. It measures implied volatility against realized volatility at several horizons, adds option-market…

This analysis checks whether daily option data can support a weekly strategy that sells at-the-money straddles on S&P 500 constituents, delta hedges shares, and holds contracts to expiration. It explains how calls and puts form a straddle, how implied and…

This pipeline constructs financial features for an ETF deployment workflow from OHLCV prices and a yield curve. It derives returns and risk-adjusted returns across multiple lookback periods, momentum acceleration and volatility ratios, then adds common…

This notebook develops model-based features for crypto perpetual futures: per-asset conditional volatility forecasts from GJR-GARCH and a market-wide stressed-regime probability from a two-state Gaussian hidden Markov model fitted to funding settlements.…

This notebook uses maximum favorable and adverse excursion analysis to inform triple-barrier widths from observed price paths. For a long entry at a bar’s close, it measures the best high and worst low over the following holding window; short positions…

This feasibility analysis checks whether the data and assumptions can support a weekly strategy that ranks S&P 500 stocks by at-the-money implied volatility and buys the leading shares. Options supply the signal, but positions are held in equities. The…

This notebook explores an economic data panel built from Federal Reserve Economic Data series. It establishes that the shipped panel uses calendar dates, including weekends and holidays, and shows how accompanying metadata identifies each series’ meaning,…

This document explains how wavelet decompositions and rolling spectral estimates describe financial returns at different time scales. Wavelets divide returns into components spanning progressively slower periods, making it possible to see which scales…

The notebook explains how to separate continuous price variation from jumps in intraday equity returns. It estimates daily realized variance from squared returns and uses bipower variation as a jump-robust estimate of the continuous component; their…

This educational treatment compares parametric stochastic models and bootstrap methods for generating synthetic financial paths. It covers geometric Brownian motion, jump diffusion, mean reversion, Heston stochastic volatility, and GARCH, alongside…

This notebook screens candidate features for a strategy that sells at-the-money call and put options on the same stock with the same expiry, holding the straddle to expiration. For each feature, it measures whether the feature ranks available names in the…

This notebook builds forward return labels for short at-the-money straddles on S&P 500 stocks. Because the daily 30-day straddle panel rolls to a different strike or expiration each session, a shifted price series would compare different contracts. Instead,…

The notebook explains Value at Risk (VaR), which marks a loss quantile, and Conditional Value at Risk (CVaR), which averages losses beyond that threshold. Using daily ETF returns, it compares historical, Gaussian, Cornish–Fisher-adjusted, and Student-t Monte…

This notebook develops a simulated market-making task in which a PPO agent chooses quote skew and spread width. Fill probability declines as quotes move farther from the mid price, while order imbalance affects both fills and subsequent price moves. A…

This teaching notebook compares target-label methods for supervised trading models using ETF data. It covers fixed-horizon returns and direction labels, rolling time-series percentiles, cross-sectional percentiles, triple-barrier labels with fixed or…

This notebook compares three ways to use market regimes in forecasting: a baseline model without a regime input, a single model given the filtered probability of a volatile state, and separate models trained within hard regime assignments. To avoid…