Per-security options recommendations generated from a 20+ strategy library using Black-Scholes pricing, terminal-payoff scenario sweeps, and a tier-aware selection rubric. Each recommendation is filtered by AI confidence (≥60%), IV regime, liquidity, cap tier (≥mid-cap), and event proximity. Strategies ranked by composite score (EV, POP, capital efficiency, AI alignment).
Strategy library: 20+ canonical structures spanning single-leg, vertical spreads, volatility plays (straddles/strangles), range-bound (iron condors/butterflies), time-based (calendars/diagonals), hedging (collars/protective puts), synthetics, asymmetric (jade lizard), and income (covered call, CSP, PMCC).
Selection rubric: Each candidate strategy is matched against the security's profile via a decision tree on (direction × IV regime × confidence × event proximity). High IV favors premium-selling (credit spreads, iron condors); low IV favors premium-buying (long options, debit spreads, long straddles). Pre-event windows block debit strategies (IV crush risk) and prefer calendar spreads.
Pricing: Black-Scholes (Hull, continuous-dividend variant) with per-leg Greeks computed analytically. Position-level Greeks aggregated by sign + qty.
Probability of profit (POP): Terminal-payoff sweep across ±50% of spot, probability-weighted using log-normal terminal distribution under risk-neutral drift.
Expected value (EV): Closed-form integration of payoff × terminal density across ±3σ in log-price (100 steps).
Composite score: 25% normalized EV + 20% POP + 10% capital efficiency + 15% AI alignment + 20% EV-per-dollar − complexity penalty − tail-risk penalty (for undefined-risk structures).
Eligibility gates: cap tier ≥ mid (micro/nano excluded for liquidity); AI confidence ≥ 60%; liquidity score ≥ Normal; no debit strategies within 7 days of earnings.
Practitioner conventions: 30-45 DTE sweet spot for credit spreads; 16-delta short strikes for high-POP credit (~84% POP); manage at 50% max profit (Tastytrade ~50K-trade study).
Academic basis: Black-Scholes (1973), Merton (1973), Heston (1993), Andersen-Bollerslev (1998), Carr-Madan (1999), Bondarenko (2014), Bali-Cakici-Whitelaw (2011), Natenberg, McMillan.
Live data integrations: ATM-straddle IV pulled from Tradier options chain when available (per-row label shows "live ATM straddle" vs. "realized-vol proxy"); earnings dates from FMP earnings-calendar API gate debit strategies in the 7-day pre-earnings window; portfolio holdings (from local store) gate covered-call / collar / protective-put eligibility; portfolio NAV computed from holdings drives capital-efficiency scoring.
Limitations: when neither Tradier nor a fallback IV feed is reachable, realized vol is used as IV proxy (clearly labeled in detail row); slippage and commission costs are not deducted from displayed EV; assignment risk for short ITM options not modeled; weekly options excluded (DTE ≥ 14 enforced); FMP earnings-calendar coverage is strongest for US-listed mega/large/mid caps (other listings may show null earningsDays).