{"uid":"cap_Qq22MrUG40X1IiEi7zHH_","slug":"black-scholes-european-option-calculator-price-greeks-iv-fa531774","name":"Black-Scholes European Option Calculator (Price, Greeks, IV)","description":"Black-Scholes European option calculator: fair price, all greeks (delta, gamma, vega, theta, rho), or implied volatility from a market price. Pure computation over your inputs.","url":"https://api.agentstools.dev/quant/options?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","HEAD","DELETE"],"type":"string"},"queryParams":{"type":"object","required":["op","S","K","T","r"],"properties":{"K":{"type":"number","description":"Strike price (> 0)"},"S":{"type":"number","description":"Spot price of the underlying (> 0)"},"T":{"type":"number","description":"Time to expiry in years (> 0)"},"q":{"type":"number","description":"Continuous dividend yield as a decimal, default 0"},"r":{"type":"number","description":"Risk-free rate, continuous, as a decimal"},"op":{"enum":["price","greeks","iv"],"type":"string","description":"price returns the fair value; greeks returns price plus all greeks; iv solves for implied volatility"},"type":{"enum":["call","put"],"type":"string","description":"Option type, default call"},"sigma":{"type":"number","description":"Volatility as a decimal (needed for price and greeks)"},"market_price":{"type":"number","description":"Observed option price, used for op=iv instead of sigma"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object"}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","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":{"p10Cents":"0.3000","medianCents":"0.3000","p90Cents":"0.3000","minCents":"0.3000","maxCents":"0.3000","p95Cents":"0.3000","sampleCount":1,"varies":false,"failureChargeRate":1},"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_ang-mh_mMQTDoqhUJ6p43","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes Black-Scholes fair price, all Greeks (delta, gamma, vega, theta, rho), or implied volatility for a European option given market parameters.","exampleAgentPrompt":"Using Black-Scholes, give me the full greeks for a European call option with spot price $150, strike $155, 0.25 years to expiry, risk-free rate 5%, and implied vol of 20%.","exampleUseCases":null,"resultDescription":"Returns a JSON object containing the computed result(s) for the requested operation: for 'price' — the Black-Scholes fair value; for 'greeks' — the fair price plus delta, gamma, vega, theta, and rho; for 'iv' — the implied volatility solved from the observed market price.","failureModes":["Missing required parameters (op, S, K, T, r) returns a 400 error","sigma not provided for price or greeks operation returns an error","market_price not provided for iv operation returns an error","Non-positive values for S, K, or T return a validation error","IV solve fails to converge if market_price is outside arbitrage bounds","Payment not included or insufficient USDC returns 402 Payment Required"],"whenToPreferThis":"Use this endpoint when you need fast, pure-computation Black-Scholes analytics for European options — pricing, full Greek sensitivities, or implied volatility inversion — without requiring a brokerage account or market data subscription. Ideal for quant agents doing real-time derivatives analysis, hedging calculations, or risk management tasks.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-11T18:38:24.461Z","isFirstParty":false,"canonicalSlug":"black-scholes-european-option-calculator-price-greeks-iv-fa531774"}