{ "x402Version": 2, "id": 8868, "slug": "8868", "resource": "https://derivatives-pricer-production.up.railway.app/v1/option/price", "description": "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.", "type": "http", "accepts": [ { "scheme": "exact", "network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp", "payTo": "DCi9X5mmacNGLeJvCw9fdWgX3G8V4QquDn4EuXATkcYr", "asset": "EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v", "amount": "10000", "maxTimeoutSeconds": 300 }, { "scheme": "exact", "network": "eip155:8453", "payTo": "0x34cfb8bdbf16e4484b7da0ed31deed5771b16c8f", "asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913", "amount": "10000", "maxTimeoutSeconds": 300 } ], "outputSchema": { "bazaar": { "info": { "input": { "body": { "dividendYield": 0, "optionType": "call", "rate": 0.05, "spot": 100, "strike": 100, "timeToExpiry": 1, "volatility": 0.2 }, "bodyType": "json", "method": "POST", "type": "http" }, "output": { "example": { "computedAt": "2026-01-01T00:00:00.000Z", "greekConvention": "raw", "greeks": { "delta": 0.63683059, "gamma": 0.01876202, "rho": 53.23248343, "theta": -6.41402764, "vega": 37.52403469 }, "greeksQuality": "analytic", "inputs": { "dividendYield": 0, "greekConvention": "raw", "model": "bsm", "optionStyle": "european", "optionType": "call", "rate": 0.05, "spot": 100, "strike": 100, "timeToExpiry": 1, "volatility": 0.2 }, "model": "black-scholes-merton", "optionStyle": "european", "price": 10.45057562, "requestId": "00000000-0000-4000-8000-000000000001", "timeline": { "calendarYearsToExpiry": 1, "effectiveStart": "2026-01-01T00:00:00.000Z", "expiration": "2027-01-01T06:00:00.000Z", "forwardStart": "2026-01-01T00:00:00.000Z", "tauYears": 1, "yearBasis": "ACT/365.25" }, "units": { "delta": "dV/dS or dV/dF (share / forward equivalent)", "gamma": "d²V/dS² or d²V/dF²", "price": "option value in spot/forward currency units", "rho": "dV/dr per 1.0 absolute rate (not per 1%)", "theta": "dV/dT per year (not per day)", "vega": "dV/dσ per 1.0 absolute volatility (not per 1%)" } }, "type": "json" } }, "schema": { "$schema": "https://json-schema.org/draft/2020-12/schema", "properties": { "input": { "additionalProperties": false, "properties": { "body": { "properties": { "dividendYield": { "description": "Continuous dividend / convenience / yield q (≥ 0, default 0).", "examples": [ 0, 0.02 ], "minimum": 0, "type": "number" }, "expiration": { "description": "ISO-8601 end of vol/exercise window. Mutually exclusive with timeToExpiry.", "format": "date-time", "type": "string" }, "forwardStart": { "description": "ISO-8601 start of vol/exercise window. If ≤ now, behaves like plain option to expiration.", "format": "date-time", "type": "string" }, "optionStyle": { "default": "european", "description": "Exercise style (default \"european\"). American uses CRR binomial with early exercise.", "enum": [ "european", "american" ], "type": "string" }, "optionType": { "description": "Call or put.", "enum": [ "call", "put" ], "type": "string" }, "rate": { "description": "Continuously compounded risk-free rate r (e.g. 0.05 = 5%). For futures-style early exercise set r≈dividendYield.", "examples": [ 0.03, 0.05 ], "type": "number" }, "spot": { "description": "Underlying price S (> 0). Equity spot OR power/commodity forward mark for the option's window.", "examples": [ 100, 82.5, 45.5 ], "exclusiveMinimum": 0, "type": "number" }, "strike": { "description": "Strike price K (> 0) in the same units as spot.", "examples": [ 100, 50 ], "exclusiveMinimum": 0, "type": "number" }, "timeToExpiry": { "description": "Time to expiry T in years (≥ 0). Required unless expiration is set. Mutually exclusive with expiration.", "examples": [ 0.25, 1 ], "minimum": 0, "type": "number" }, "treeSteps": { "description": "CRR steps for American (default 200 on single price).", "maximum": 500, "minimum": 50, "type": "integer" }, "volatility": { "description": "Annualized volatility σ as a decimal (> 0). Applies over the vol-accrual window τ.", "examples": [ 0.15, 0.2, 0.45 ], "exclusiveMinimum": 0, "type": "number" } }, "required": [ "spot", "strike", "rate", "volatility", "optionType" ] }, "bodyType": { "enum": [ "json", "form-data", "text" ], "type": "string" }, "method": { "enum": [ "POST" ], "type": "string" }, "type": { "const": "http", "type": "string" } }, "required": [ "type", "method", "bodyType", "body" ], "type": "object" }, "output": { "properties": { "example": { "description": "Fair value and Greeks. European Greeks are analytic BSM; American Greeks are finite-difference on the CRR tree. timeline.tauYears is the model life (window); calendarYearsToExpiry is purchase→expiry.", "properties": { "computedAt": { "description": "ISO-8601 UTC timestamp of computation", "type": "string" }, "greeks": { "description": "Greeks for hedge construction", "properties": { "delta": { "description": "∂V/∂S", "type": "number" }, "gamma": { "description": "∂²V/∂S²", "type": "number" }, "rho": { "description": "∂V/∂r per 1.0 absolute rate", "type": "number" }, "theta": { "description": "∂V/∂T per year", "type": "number" }, "vega": { "description": "∂V/∂σ per 1.0 absolute vol", "type": "number" } }, "required": [ "delta", "gamma", "vega", "theta", "rho" ], "type": "object" }, "greeksQuality": { "enum": [ "analytic", "finite-difference" ], "type": "string" }, "inputs": { "description": "Echo of validated request inputs (timeToExpiry may be resolved τ)", "type": "object" }, "model": { "enum": [ "black-scholes-merton", "binomial-crr-american" ], "type": "string" }, "optionStyle": { "enum": [ "european", "american" ], "type": "string" }, "price": { "description": "Model option fair value in underlying currency units", "type": "number" }, "requestId": { "description": "Correlation id for this call", "type": "string" }, "timeline": { "description": "Resolved ACT/365.25 window", "type": "object" }, "treeSteps": { "type": "integer" }, "units": { "description": "Human/agent readable unit notes for price and Greeks", "type": "object" } }, "required": [ "price", "greeks", "inputs", "model", "optionStyle", "timeline", "greeksQuality", "requestId", "computedAt" ], "title": "OptionPriceResponse", "type": "object" }, "type": { "type": "string" } }, "required": [ "type" ], "type": "object" } }, "required": [ "input" ], "type": "object" } } }, "tags": [ "bazaar" ], "sourceHost": "derivatives-pricer-production.up.railway.app", "lastUpdated": "2026-09-14T19:54:48.07Z", "quality": { "calls30d": 2, "uniquePayers30d": 2, "lastCalledAt": "2026-09-14T19:54:47.81Z" }, "liveness": {}, "verified": false, "featured": false, "provider": { "host": "derivatives-pricer-production.up.railway.app", "manifest_name": "derivatives-pricer-production.up.railway.app", "source": "cdp-mirror", "source_manifest_url": "https://api.cdp.coinbase.com/platform/v2/x402/discovery/resources", "submitted_at": "2026-09-18T22:00:31.484Z" } }