# Black-Scholes Option Pricing & Greeks Calculator > Black-Scholes Option Pricing & Greeks Calculator is a paid API for AI agents from agent-data-tools.revmesh2074.workers.dev, paid per call via x402, $0.01/call, status unknown (last checked 2026-11-07). Prices European call and put options using Black-Scholes-Merton and returns delta, gamma, vega, theta, rho, d1, d2, probability ITM, and implied volatility ## Facts - Endpoint: GET https://agent-data-tools.revmesh2074.workers.dev/options/price?utm_source=zero.xyz - Price: $0.01/call - Payment: x402 - Status: unknown - Last checked: 2026-11-07 - Activations on Zero: 0 - Provider: agent-data-tools.revmesh2074.workers.dev - Website: https://agent-data-tools.revmesh2074.workers.dev - Tags: x402 - Canonical page: https://www.zero.xyz/c/agent-data-tools-revmesh2074-workers-dev-black-scholes-option-pricing-15a6f412 - Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_20GwhUuNoOOzxLsJFwh2p Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently. ## How to call it through Zero Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`): ```sh zero fetch --capability agent-data-tools-revmesh2074-workers-dev-black-scholes-option-pricing-15a6f412 ``` Example prompt: Price a European call and put on a stock with spot 150, strike 155, 45 days to expiry, 25% annual volatility, and a 5% risk-free rate — give me the Black-Scholes prices and all the Greeks including delta, gamma, vega, theta, and the probability of ending in the money. ## When to prefer this Use this endpoint when you need fast, self-contained Black-Scholes pricing and Greeks for European vanilla options without needing a live market data feed. It is ideal for crypto, stock, or FX options where you already have the spot, vol, and rate inputs. Prefer it over data-vendor option chains when you want pure arithmetic — no latency from external data sources. It is the right choice for hedge sizing, quote validation, implied vol extraction, and risk reporting in automated agent workflows. ## Known failure modes - Missing required spot or strike parameters returns an error - Supplying a market price that implies a negative or extreme implied volatility may fail to converge - Invalid expiry date format causes a parse error - Volatility or rate values outside reasonable bounds may produce numerical edge cases - Negative spot or strike values are not meaningful and may error ## How this service works Option pricing, Black-Scholes. Price a European call and put with Black-Scholes-Merton and get delta, gamma, vega (per vol point), theta (per day), rho, d1, d2 and the probability of ending in the money; or give a market price and get the implied volatility. Inputs: spot, strike, expiry date or days, volatility, interest rate and dividend or funding yield in percent. Pure arithmetic, no data source. Use for crypto, stock or FX options, to price a quote or size a hedge. ## Output Returns a JSON object with d1, d2, the model name, echoed inputs, and nested call and put objects each containing: price, delta, gamma, vega (per vol point), theta (per day), rho, and probabilityItm. If a market price is supplied, returns the implied volatility instead. ## Request schema (JSON Schema) ```json { "type": "object", "$schema": "https://json-schema.org/draft/2020-12/schema", "required": [ "input" ], "properties": { "input": { "type": "object", "required": [ "type", "method" ], "properties": { "type": { "type": "string", "const": "http" }, "method": { "enum": [ "GET" ], "type": "string" }, "queryParams": { "type": "object", "required": [ "spot", "strike" ], "properties": { "vol": { "type": "number", "examples": [ 20 ], "description": "Annual volatility in percent, e.g. 20 (default 50); not needed with price" }, "days": { "type": "number", "examples": [ 365 ], "description": "Days to expiry (default 30), or give expiry or years" }, "rate": { "type": "number", "examples": [ 5 ], "description": "Risk-free rate in percent per year, e.g. 5 for 5% (default 0)" }, "spot": { "type": "number", "examples": [ 100 ], "description": "Price of the underlying" }, "type": { "type": "string", "examples": [ "call" ], "description": "call or put, for the implied volatility (default call)" }, "price": { "type": "number", "examples": [ 10.45 ], "description": "A market option price: returns the implied volatility" }, "years": { "type": "number", "examples": [ 1 ], "description": "Years to expiry, instead of days" }, "expiry": { "type": "string", "examples": [ "2026-12-18" ], "description": "Expiry date (ISO), instead of days" }, "strike": { "type": "number", "examples": [ 100 ], "description": "Strike price" }, "dividend": { "type": "number", "examples": [ 0 ], "description": "Dividend, funding or borrow yield in percent per year (default 0)" } } } }, "additionalProperties": false }, "output": { "type": "object", "required": [ "type" ], "properties": { "type": { "type": "string" }, "example": { "type": "object", "properties": { "d1": { "type": "number" }, "d2": { "type": "number" }, "pu … (truncated) ``` ## Response schema (JSON Schema) ```json { "type": "json", "example": { "d1": 0.35, "d2": 0.15, "put": { "rho": -0.418905, "vega": 0.37524, "delta": -0.363169, "gamma": 0.018762, "price": 5.573526, "theta": -0.004542, "probabilityItm": 0.440382 }, "call": { "rho": 0.532325, "vega": 0.37524, "delta": 0.636831, "gamma": 0.018762, "price": 10.450584, "theta": -0.017573, "probabilityItm": 0.559618 }, "model": "Black-Scholes-Merton (European exercise)", "inputs": { "vol": 0.2, "rate": 0.05, "spot": 100, "years": 1, "strike": 100, "dividend": 0 } } } ``` ## More - Live health (JSON, refreshed every minute): https://www.zero.xyz/c/agent-data-tools-revmesh2074-workers-dev-black-scholes-option-pricing-15a6f412/health.json - [Zero catalog index](https://www.zero.xyz/llms.txt) - [Other services from agent-data-tools.revmesh2074.workers.dev](https://www.zero.xyz/host/agent-data-tools.revmesh2074.workers.dev/llms.txt)