{"uid":"cap_rE8D1XvD-TqKBFOBmARnG","slug":"black-scholes-options-pricer-949a3559","name":"Black-Scholes Options Pricer","description":"European call/put fair value plus delta, gamma, theta, vega, rho from spot, strike, days-to-expiry, rate and volatility; optional implied-vol solve if market_price supplied.","url":"https://api.24klabs.ai/api/black-scholes-options-pricer?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"rate":{"type":"number"},"spot":{"type":"number"},"type":{"type":"string"},"strike":{"type":"number"},"volatility":{"type":"number"},"days_to_expiry":{"type":"number"}}},"responseSchema":{"type":"json","example":{"delta":0.28,"gamma":0.05,"price":0.94}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.005","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":"$0.005/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.005","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.005","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_G9EwESuDMN9yr6Sv3xGsK","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.005","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Prices European call/put options (fair value + Greeks) using Black-Scholes, with optional implied volatility solve from a market price.","exampleAgentPrompt":"What's the Black-Scholes fair value and all the Greeks for a European call option with a spot price of $150, strike of $155, 45 days to expiry, 5% risk-free rate, and 25% implied volatility?","exampleUseCases":[{"title":"Options trader hedging portfolio","prompt":"I need to price a European put on a stock trading at $200 with a $195 strike, 30 days to expiry, 4.5% rate, and 30% volatility — give me the fair value plus delta and gamma so I know how to hedge."},{"title":"Implied volatility extraction from live price","prompt":"The market is quoting a call option at $8.50 — spot is $100, strike is $102, 21 days to expiry, 5% rate. Can you back out the implied volatility from that price?"},{"title":"Options sensitivity analysis for risk report","prompt":"I'm building a risk report and need theta, vega, and rho for a European call with spot $500, strike $520, 60 days to expiry, 4% risk-free rate, and 20% volatility."}],"resultDescription":"Returns the theoretical fair value of the European call or put option, plus the five standard Greeks: delta (directional sensitivity), gamma (delta curvature), theta (time decay), vega (volatility sensitivity), and rho (rate sensitivity). If a market_price is supplied, also returns the implied volatility solved from that price.","failureModes":["Missing required fields (spot, strike, DTE, rate, volatility) returns a 400 error","Negative or zero spot/strike/DTE values may cause computation errors","Extremely deep in-the-money or out-of-the-money options may produce near-zero Greeks with precision caveats","Implied vol solve may fail to converge if market_price is below intrinsic value or otherwise arbitrage-free bounds are violated","Payment failure (insufficient USDC balance or x402 auth issue) returns a 402 error"],"whenToPreferThis":"Choose this endpoint when you need fast, reliable Black-Scholes pricing and Greeks for European-style options without standing up your own quant library. Ideal for agents doing real-time hedging analysis, building risk reports, or extracting implied volatility from observed market prices. Not suitable for American options (which require binomial or finite-difference methods) or exotic payoffs.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-12T18:51:33.433Z","isFirstParty":false,"canonicalSlug":"black-scholes-options-pricer-949a3559"}