{"uid":"cap_0wx-qz6ggSu8tMsVPwpSa","slug":"black-scholes-greeks-f1bb5a81","name":"Black-Scholes Greeks","description":"European option price (call and put) with delta, gamma, vega, theta and rho via Black-Scholes.","url":"https://164.160.90.241.sslip.io/api/math-black-scholes-greeks?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","time","rate","vol"],"properties":{"vol":{"type":"number","description":"Volatility as decimal"},"rate":{"type":"number","description":"Risk-free rate as decimal"},"spot":{"type":"number","description":"Underlying price"},"time":{"type":"number","description":"Years to expiry"},"strike":{"type":"number","description":"Strike"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object"}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","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":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_pBm7QoyNdZU_h6plc_AvP","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes European option call and put prices plus all five Greeks (delta, gamma, vega, theta, rho) using the Black-Scholes model","exampleAgentPrompt":"Can you calculate the Black-Scholes price and all five Greeks for a European call and put with spot at 100, strike at 105, 0.25 years to expiry, a risk-free rate of 5%, and volatility of 20%?","exampleUseCases":[{"title":"Options desk pre-trade pricing","prompt":"I'm about to trade a European option — spot is 150, strike 155, expiry in 0.5 years, risk-free rate 4.5%, implied vol 18%. Give me the Black-Scholes call and put prices plus all the Greeks before I put the order in."},{"title":"Hedging delta-neutral portfolio","prompt":"I need the delta and gamma for a European put with spot at 200, strike 195, 3 months to expiry, risk-free rate 3%, and vol 25% so I can figure out how many shares to hold to stay delta-neutral."},{"title":"Sensitivity analysis for rates change","prompt":"What happens to my option's rho if I have a European call with spot 80, strike 85, one year to expiry, current risk-free rate 2%, and volatility 30%? Give me the full Greeks breakdown."}],"resultDescription":"Returns the theoretical call and put prices calculated via Black-Scholes, along with all five Greeks: delta (price sensitivity to spot), gamma (rate of change of delta), vega (sensitivity to volatility), theta (time decay), and rho (sensitivity to interest rate), all as numeric values.","failureModes":["Missing required parameters (spot, strike, time, rate, vol) returns a validation error","Non-positive time to expiry or volatility may produce NaN or error responses","Extreme parameter values (e.g., very deep in/out of the money) may produce near-zero or near-1 Greeks","Network or upstream server unavailability returns HTTP 5xx","Invalid non-numeric query parameter types return a 400 bad request"],"whenToPreferThis":"Choose this endpoint when you need a fast, authoritative Black-Scholes calculation for European options covering all five Greeks in a single call. Prefer it over manual computation or general math sandboxes when you need structured, labeled outputs for delta, gamma, vega, theta, and rho alongside the option price. It is not suitable for American options (early exercise), exotic options, or models beyond Black-Scholes (e.g., binomial trees, Monte Carlo).","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-12T00:41:28.474Z","isFirstParty":false,"canonicalSlug":"black-scholes-greeks-f1bb5a81"}