{"uid":"cap_zXCqCzTmKYlGkeaJOV3YN","slug":"agentstoolshub-european-option-pricing-black-scholes-merton-53ab4db2","name":"AgentsToolsHub European Option Pricing (Black-Scholes-Merton)","description":"European option pricing with the Black-Scholes-Merton model: exact price for calls and puts plus delta, gamma, theta, vega and rho, with dividend yield support. Deterministic closed-form math — the numbers agents should quote instead of hallucinating option values. Use this when an agent needs to black-Scholes price + all five Greeks.","url":"https://agentstoolshub.com/api/v1/finance/option-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","years","volPct"],"properties":{"spot":{"type":"number","description":"Spot price"},"type":{"enum":["call","put"],"type":"string","description":"Type"},"years":{"type":"number","description":"Time to expiry (years)"},"strike":{"type":"number","description":"Strike"},"volPct":{"type":"number","description":"Volatility (%)"},"ratePct":{"type":"number","description":"Risk-free rate (%)"},"divYieldPct":{"type":"number","description":"Dividend yield (%)"}}}},"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":null,"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_lGfUsRJ3EFAd6mOF-zq6d","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 exact European option price (call or put) and all five Greeks (delta, gamma, theta, vega, rho) using the Black-Scholes-Merton closed-form model, with optional dividend yield support.","exampleAgentPrompt":"What's the Black-Scholes price and all five Greeks for a European call option with a spot price of $150, strike of $155, 45 days to expiry, implied volatility of 28%, and a risk-free rate of 5%?","exampleUseCases":[{"title":"Options desk pre-trade valuation","prompt":"Price a European put option using Black-Scholes: spot is $200, strike is $195, time to expiry is 0.25 years, implied vol is 22%, risk-free rate is 4.5%, and dividend yield is 1.2%. I need the price plus all five Greeks."},{"title":"Portfolio delta-hedging calculation","prompt":"I need the delta and gamma for a European call option — spot $320, strike $330, 60 days to expiry expressed as years (about 0.164), vol at 35%, risk-free rate 5.25%, no dividends. What hedge ratio do I need?"},{"title":"Options strategy sensitivity analysis","prompt":"Can you calculate vega and theta for a European call with spot $80, strike $85, 0.5 years to expiry, 30% volatility, 4% risk-free rate, and 2% dividend yield? I want to understand how much my position decays and moves with vol."}],"resultDescription":"Returns the theoretical price of the European option (call or put) and all five Greeks: delta (price sensitivity to spot), gamma (rate of change of delta), theta (time decay), vega (sensitivity to volatility), and rho (sensitivity to interest rates), computed via the exact Black-Scholes-Merton closed-form formula.","failureModes":["Missing required parameters (spot, strike, years, volPct) returns a 400 error","Negative or zero time-to-expiry may produce undefined or degenerate outputs","Extremely high or low volatility values may produce near-boundary pricing","Non-numeric query parameter values return validation errors","Invalid option type (not 'call' or 'put') returns an enum validation error"],"whenToPreferThis":"Use this endpoint when you need exact, deterministic European option pricing via the Black-Scholes-Merton closed-form model rather than numerical approximations or simulation. Ideal when all five Greeks are needed simultaneously alongside the price. Prefer this over Monte Carlo or binomial tree approaches when the option is European-style (no early exercise) and when speed and determinism matter. The dividend yield parameter makes it suitable for equity options on dividend-paying stocks.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-17T12:40:57.750Z","isFirstParty":false,"canonicalSlug":"agentstoolshub-european-option-pricing-black-scholes-merton-53ab4db2"}