{"uid":"cap__4px2yV7tCnw2SEpgg-w9","slug":"black-scholes-options-pricer-greeks-calculator-6d18ea61","name":"Black-Scholes Options Pricer & Greeks Calculator","description":"X402 micropayments server — AI agents pay USDC for OFAC screening, rates, and billing verification.","url":"https://x402helper.xyz/89e509/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"],"type":"string"},"queryParams":{"type":"object","required":["op","S","K","T","r"],"properties":{"K":{"type":"number","default":null,"description":"Strike price (> 0)"},"S":{"type":"number","default":null,"description":"Spot price of the underlying (> 0)"},"T":{"type":"number","default":null,"description":"Time to expiry in years (> 0)"},"q":{"type":"number","default":null,"description":"Continuous dividend yield as a decimal, default 0"},"r":{"type":"number","default":null,"description":"Risk-free rate, continuous, as a decimal"},"op":{"enum":["price","greeks","iv"],"type":"string","default":null,"description":"price returns the fair value; greeks returns price plus all greeks; iv solves for implied volatility"},"type":{"enum":["call","put"],"type":"string","default":null,"description":"Option type, default call"},"sigma":{"type":"number","default":null,"description":"Volatility as a decimal (needed for price and greeks)"},"market_price":{"type":"number","default":null,"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":{"type":"json","example":{"result":{},"success":true}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.004","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":"$0.004/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.004","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.004","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_Km8H0aYEUW1_ZGZE4X0LU","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.004","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes fair value, Greeks (delta, gamma, theta, vega, rho), or implied volatility for European options using the Black-Scholes model.","exampleAgentPrompt":"Price a European call option where the stock is at $150, the strike is $155, it expires in 0.25 years, the risk-free rate is 5%, and volatility is 20% — give me the fair value.","exampleUseCases":[{"title":"Options fair value before trading","prompt":"What's the Black-Scholes fair value of a call option on a stock trading at $200, strike $210, expiring in 6 months (0.5 years), risk-free rate 4.5%, and implied vol of 25%?"},{"title":"Full Greeks for risk management","prompt":"Give me the full Greeks — delta, gamma, theta, vega, rho — for a put option with spot $100, strike $95, 3 months to expiry (0.25 years), risk-free rate 3%, and sigma 18%."},{"title":"Implied volatility from market price","prompt":"Solve for implied volatility on a call option currently trading at $8.50 in the market, spot price $130, strike $135, 45 days to expiry (0.123 years), and risk-free rate 5%."}],"resultDescription":"Returns a JSON object with success=true and a result object containing the computed output: for op=price, the theoretical option price; for op=greeks, the price plus all Greeks (delta, gamma, theta, vega, rho); for op=iv, the implied volatility as a decimal.","failureModes":["Missing required parameters (op, S, K, T, r) returns an error","sigma missing when op=price or op=greeks (needed for computation)","market_price missing when op=iv","S, K, or T <= 0 (invalid domain) returns an error","Non-numeric parameter values cause parsing errors","Network or payment failure results in HTTP 402 if USDC not provided"],"whenToPreferThis":"Choose this endpoint when you need fast, mathematically rigorous Black-Scholes pricing, Greeks, or implied volatility for European options without standing up your own quant infrastructure. Ideal for AI agents that need on-demand options analytics at low cost ($0.004/call via x402 micropayments) without API keys or subscriptions.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-31T18:42:12.030Z","isFirstParty":false,"canonicalSlug":"black-scholes-options-pricer-greeks-calculator-6d18ea61"}