{"uid":"cap_20GwhUuNoOOzxLsJFwh2p","slug":"agent-data-tools-revmesh2074-workers-dev-black-scholes-option-pricing-15a6f412","name":"Black-Scholes Option Pricing & Greeks Calculator","description":"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.","url":"https://agent-data-tools.revmesh2074.workers.dev/options/price?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"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"},"put":{"type":"object","properties":{"rho":{"type":"number"},"vega":{"type":"number"},"delta":{"type":"number"},"gamma":{"type":"number"},"price":{"type":"number"},"theta":{"type":"number"},"probabilityItm":{"type":"number"}}},"call":{"type":"object","properties":{"rho":{"type":"number"},"vega":{"type":"number"},"delta":{"type":"number"},"gamma":{"type":"number"},"price":{"type":"number"},"theta":{"type":"number"},"probabilityItm":{"type":"number"}}},"model":{"type":"string"},"inputs":{"type":"object","properties":{"vol":{"type":"number"},"rate":{"type":"number"},"spot":{"type":"number"},"years":{"type":"number"},"strike":{"type":"number"},"dividend":{"type":"number"}}}}}}}}},"responseSchema":{"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}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.01","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.01/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.01","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.01","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_bCiZOIHC_VUptQ78my7yh","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.01","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":"agent-data-tools.revmesh2074.workers.dev","brandSlug":"agent-data-tools-revmesh2074-workers-dev-x402","brandBaseUrl":"https://agent-data-tools.revmesh2074.workers.dev","brandDocsUrl":null,"whatItDoes":"Prices European call and put options using Black-Scholes-Merton and returns delta, gamma, vega, theta, rho, d1, d2, probability ITM, and implied volatility","exampleAgentPrompt":"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.","exampleUseCases":[{"title":"Crypto options hedge sizing","prompt":"I'm short a Bitcoin call with spot at 65000, strike 70000, 21 days to expiry, implied vol of 80%, and a 0% rate — give me the Black-Scholes price and delta so I can size my hedge."},{"title":"Implied volatility extraction","prompt":"The market is quoting a call on AAPL at $4.20, spot is 180, strike 182, 14 days to expiry, and the risk-free rate is 5.3% — can you back out the implied volatility?"},{"title":"FX option theta decay check","prompt":"I have a EUR/USD put with spot 1.0850, strike 1.0750, 7 days to expiry, vol 8%, and a 0% dividend yield — what's the Black-Scholes put price and how much theta am I losing per day?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-07T06:45:47.792Z","isFirstParty":false,"canonicalSlug":"agent-data-tools-revmesh2074-workers-dev-black-scholes-option-pricing-15a6f412"}