{"uid":"cap_8eAvJtZUXoKR1_yW6XQvi","slug":"option-pricer-greeks-black-scholes-5cb37563","name":"Option Pricer & Greeks (Black-Scholes)","description":"Black-Scholes price and greeks (delta, gamma, vega, theta, rho) of a European call or put, probability in the money and breakeven; or the implied volatility from a market price. For stocks, FX or crypto.","url":"https://bess-x402.onrender.com/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","HEAD","DELETE"],"type":"string"},"queryParams":{"type":"object","required":["spot","strike","days"],"properties":{"days":{"type":"number","description":"Days to expiry"},"kind":{"type":"string","description":"call or put"},"spot":{"type":"number","description":"Underlying price"},"strike":{"type":"number","description":"Strike price"},"rate_pct":{"type":"number","description":"Risk-free rate in % (default 4)"},"market_price":{"type":"number","description":"Option market price, to solve for implied volatility"},"volatility_pct":{"type":"number","description":"Annual volatility in % (omit when giving market_price)"},"dividend_yield_pct":{"type":"number","description":"Dividend or carry yield in %"}}}},"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":"$0.002/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.002","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.002","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_-w9F2GcHXnvLKUeON9uND","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.002","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Calculates Black-Scholes price, Greeks (delta, gamma, vega, theta, rho), probability in the money, and breakeven for European call/put options, or solves for implied volatility from a market price.","exampleAgentPrompt":"Price a European call option on a stock trading at $150, with a $155 strike, 30 days to expiry, and 25% annual volatility at a 4% risk-free rate — give me the Black-Scholes price and all the Greeks.","exampleUseCases":[{"title":"Options trader checking live Greeks","prompt":"I'm looking at a put option on a stock at $200 spot, $195 strike, 45 days to expiry, 30% vol, and the risk-free rate is 5%. Can you give me the full Black-Scholes breakdown — price, delta, gamma, vega, theta, and the probability it expires in the money?"},{"title":"Implied volatility from market price","prompt":"A call option on BTC with a $65,000 strike and spot at $63,000 is trading in the market at $2,400. It expires in 21 days and the risk-free rate is 4%. What implied volatility does that market price imply?"},{"title":"FX option pricing for carry hedge","prompt":"Price a European call on EUR/USD: spot is 1.085, strike 1.10, 60 days to expiry, 8% annual volatility, 4% USD risk-free rate, and a 3% euro dividend yield. Show me the price and all Greeks."}],"resultDescription":"Returns the theoretical option price (premium), all five Greeks (delta, gamma, vega, theta, rho), probability of expiring in the money, and the breakeven price. When a market_price is supplied instead of volatility, it returns the implied volatility that matches the observed price.","failureModes":["Missing required parameters (spot, strike, days) returns a 400 error","Non-positive spot, strike, or days values may produce invalid results","Implied volatility solver may fail to converge if market_price is far from theoretical bounds","Negative implied volatility request when market price is below intrinsic value"],"whenToPreferThis":"Use this endpoint when you need a fast, per-call, parameterized Black-Scholes pricer for European options across stocks, FX, or crypto without setting up a local quantitative library. It is ideal when you also need the full Greek surface and probability metrics in a single call. Prefer this over general-purpose data providers when you need implied volatility solved from a live market price.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-30T12:34:15.081Z","isFirstParty":false,"canonicalSlug":"option-pricer-greeks-black-scholes-5cb37563"}