Options Strategy — model card

v1.0 · Tier 2Beta Generates AI-selected options strategy recommendations per security with rigorous Greeks, POP, and EV math.

Purpose

Recommends the optimal options strategy per security from a 21-strategy library, given the security's AI score, prescience forecast, IV regime, liquidity, cap tier, and event proximity. Drives /options page. Designed to answer: "Given my system has high conviction on TICKER, what is the best way to express that view in options?"

Inputs

• AI score (0-100) from scoring engine — drives direction bucket
• Confidence (0-100%) from scoring engine — drives strategy aggressiveness (16-delta short for high conf, 10-delta for mid)
• Prescience forecast — expectedMovePct, probUp; gates Test 5 directionality
• IV rank (0-100) — IVR > 50 favors premium-selling, IVR < 25 favors premium-buying
• Cap tier from engine/cap-tier.js — micro/nano hard-blocked (illiquid options chains)
• Liquidity score (0-100) — gates options eligibility (require Normal+ ≥ 50)
• Event proximity — earnings within 7d blocks debit strategies (IV crush)
• Spot price, IV, risk-free rate, dividend yield — Black-Scholes inputs

Architecture

Strategy library (21 canonical structures)

Spans 9 families covering the full directional / vol / income / hedging surface:

Family	Strategies
Single-leg	Long Call, Long Put, Covered Call, Cash-Secured Put
Vertical debit	Bull Call Spread, Bear Put Spread
Vertical credit	Bull Put Spread, Bear Call Spread
Volatility	Long Straddle, Long Strangle, Short Strangle
Range-bound (4-leg)	Iron Condor, Iron Butterfly
Time-based	Calendar Spread, Diagonal Spread
Hedging	Collar, Protective Put
Asymmetric	Jade Lizard
Synthetic / income	Synthetic Long Stock, Poor Man's Covered Call

Selection rubric (decision tree)

Maps (direction × IV regime × confidence × event proximity) → ordered candidate list:

Direction	IV	Event	Top candidates
Bullish	High	Clean	Bull Put Spread (16Δ) → Cash-Secured Put → Jade Lizard
Bullish	Low	Clean	Long Call → Bull Call Spread → Synthetic Long → PMCC
Bearish	High	Clean	Bear Call Spread (16Δ) → Protective Put → Collar
Bearish	Low	Clean	Long Put → Bear Put Spread
Neutral	High	Clean	Iron Condor → Iron Butterfly → Short Strangle (PM only)
Neutral	Low	Clean	Long Strangle → Long Straddle → Calendar Spread
Bullish	High	Pre-earnings	Jade Lizard → Bull Put Spread → Calendar (term-structure)
Any	High	Post-earnings	Short Strangle / Iron Condor (IV crush capture)

Eligibility gates (pre-recommendation)

• Cap tier ≥ mid — micro/nano excluded (illiquid options chains)
• AI confidence ≥ 60% — below threshold, defer (don't trade noise)
• Liquidity score ≥ 50 — Normal grade or better (deep enough for spreads)
• Earnings > 7 days — debit strategies blocked through earnings (IV crush kills them)

Pricing — Black-Scholes (Hull)

Per-leg price + Greeks via engine/options.js. Continuous-dividend variant of BS with analytic Greeks (delta, gamma, vega, theta, rho). Implied volatility back-solved via Newton-Raphson on observed market prices when an IV feed is available; otherwise realized vol is used as IV proxy.

d1 = [ln(S/K) + (r - q + σ²/2)·T] / (σ·√T)
d2 = d1 - σ·√T

Call:  C = S·e^(-q·T)·N(d1) - K·e^(-r·T)·N(d2)
Put:   P = K·e^(-r·T)·N(-d2) - S·e^(-q·T)·N(-d1)

Probability of profit (POP)

Terminal-payoff sweep across ±50% of spot at expiration; probability-weighted using log-normal terminal distribution under risk-neutral drift. POP = ∫ P(S_T) · 𝟙{pnl(S_T) > 0} dS_T integrated over the profitable region.

Expected value (EV)

Closed-form integration of payoff × density across ±3σ in log-price (100 steps):

EV = Σᵢ pnl(S_T,i) · φ(z_i) · Δz   where  S_T = S·exp(μ + σ√T·z)

Composite ranking score (0-100)

Combines five orthogonal dimensions:

• 25% — normalized EV (scaled by capital required)
• 20% — POP (probability of profit)
• 10% — capital efficiency (1 - capRequired/NAV, capped at 10%)
• 15% — alignment with AI direction (bullish/bearish/neutral match)
• 20% — EV-per-dollar (positive only)
• − complexity penalty (4% per complexity tier above 1)
• − 10% tail-risk penalty for undefined-risk structures

Practitioner conventions baked in

• 30-45 DTE sweet spot for credit spreads (Tastytrade ~50K-trade study; optimal theta vs vega balance)
• 16-delta short strikes ≈ 1σ OTM ≈ ~84% POP at entry (high-conf credit setups)
• 10-delta short strikes for mid-conf (wider POP, smaller credit)
• 1/3 width minimum credit on verticals (3:1 worst-case R:R)
• Manage at 50% max profit for credit strategies (Tastytrade convention; higher Sharpe than holding to expiration)
• Calendar/diagonal preferred for pre-event entries (term-structure play, no IV-crush exposure)

Limitations

Common pitfalls (built-in safeguards)

• Naked shorts without margin — shortStrangle requires hasPortfolioMargin flag
• Volatility crush on debits through earnings — debit strategies hard-blocked when earningsDays ≤ 7
• Long-call lottos on small caps — micro/nano cap tier hard-blocked at eligibility gate (Bali-Cakici-Whitelaw 2011: lottery preference depresses small-cap option returns)
• Doubling down on losers — recommendation is single-shot per security per session; rebalance/roll logic out of scope

Academic basis

• Black & Scholes (1973) — Closed-form European option pricing under GBM
• Merton (1973) — Extends BS to dividends, jumps, American-style
• Heston (1993) — Stochastic vol pricing; informs skew interpretation
• Andersen & Bollerslev (1998) — Realized volatility from high-freq data
• Carr & Madan (1999) — Variance swap replication; foundation of VIX
• Bondarenko (2014) — Variance risk premium (~-2% to -4% monthly on SPX puts) → theoretical basis for premium selling
• Bali, Cakici & Whitelaw (2011) — Lottery preference depresses returns on high-skew stocks
• Natenberg (2014) — "Option Volatility & Pricing" (practitioner classic)
• McMillan (2012) — "Options as a Strategic Investment" (strategy bible)

Versioning

• v1.0 (2026-04-27) — initial release. 21 strategies, decision rubric, BS pricing, POP/EV math, composite ranking, /options page launched

Source

• engine/options.js — Black-Scholes pricing + Greeks + IV (foundation)
• engine/options-strategies.js — strategy library + selection rubric + ranking
• engine/cap-tier.js — eligibility gates by cap tier
• options.html — live recommendation page