This research paper provides a rigorous mathematical analysis of four distinct algorithmic trading systems designed for the Nasdaq-100 Futures and Options ecosystem. Drawing directly from the implementation details of four specialized Python-based trading bots—(1) AI Momentum with Call Calendar Spread, (2) Call Ratio Backspread with Gamma Scalping, (3) Volatility Mean Reversion, and (4) AI CapEx Call Butterfly with Delta Hedging—this paper dissects the quantitative models, st