BSM Price+Greeks

When to use: you already have model inputs (S or forward mark, K, T, r, σ) and need fair value + hedge ratios — not market-premium IV. European BSM price + analytic Greeks (delta, gamma, vega, theta, rho). Works for equity spots and power/commodity forwards (use the maturity mark as spot). USDC exact on Solana/Base. Free fixed sample: GET /v1/demo/option-price.

When to use: one market premium → need σ̂ + Greeks; cheaper/faster than a full surface. Solves Black-Scholes IV then prices Greeks at the solved σ. Same engine as the surface endpoint (fastImpliedVol). Prefer surface when you have a multi-strike/maturity book. USDC exact on Solana/Base.

When to use: you already have an IV surface (k,T,σ) and need to price options on it — not invert premiums and not scalar σ. Interpolates total variance w=σ²T bilinear in log-moneyness k=ln(K/F); wingRule=flat_vol. Returns price, interpolated σ, k, F, BS Greeks. USDC exact on Solana/Base. Prefer /v1/option/price when σ is a single scalar.

When to use: book reval on an IV surface under F/rate/time/vol shocks with sticky moneyness|strike|fixed_vol. Vol order: interpolate → volAbs → volRel → smileTwist*k. Greeks are sticky-σ BS Greeks (not smile bump deltas). USDC exact on Solana/Base. Prefer scalar /v1/portfolio/scenario for per-leg scalar σ books.

When to use: multi-leg European book → need net MTM + net Greeks (long/short via signed quantity). Shared rate/yield; each leg has underlying, strike, T, type, quantity, vol. Optional dollar Greeks. Prefer scenario endpoint for what-if P&L. USDC exact on Solana/Base.

When to use: book of market premiums → need IV grid + per-quote Greeks (not a single contract). Shared rate/yield; each row has its own underlying (power/commodity forwards by maturity). Returns strike×maturity IV surface, fit quality, solve stats. USDC exact on Solana/Base. Prefer single IV endpoint for one premium.

When to use: what-if P&L under relative spot/vol shocks and calendar time decay on a European book. Returns base MTM+Greeks and per-scenario shocked MTM, MTM change, full Greeks. Single-option or multi-leg. USDC exact on Solana/Base.