Options Pricing Engine

What it is

Three independent vanilla-option pricers, a Black-Scholes closed form, a CRR binomial tree with American exercise, and a seeded Monte Carlo simulation, that should all agree, and a set of gates that prove whether they actually do.

Seven gates, all passing

• —Put-call parity holds to 2.84e-14 in the closed form, and across all 16 grid points in the Monte Carlo version.
• —Tree-to-Black-Scholes convergence shrinks cleanly from 200 to 2,000 steps; Monte Carlo-to-Black-Scholes convergence holds correct 95% confidence-interval coverage over 200 seeds.
• —Closed-form and finite-difference Greeks agree to 5.57e-6 relative error; no-arbitrage (American price at least the European price) holds with zero violations.

The market disagrees with all three

Turning the validated engine on a real SPY option-chain snapshot and inverting market prices back to volatility surfaces the smile: the market quotes a different sigma at every strike, spanning 13.6 to 15.9% at-the-money across a 9 to 90 day window. Flat-vol Black-Scholes says that is impossible, the smile is the market pricing in the fat tails and skew a lognormal model assumes away.

Why it matters

Built in one day via a Claude-Code-driven, subagent-based TDD plan with independent per-task review and a final adversarial whole-branch pass. A live GitHub Pages explorer with sliders for every pricing input carries a self-check badge that re-verifies all seven gates on every load, the numbers are regenerated, not hand-typed.