{"uid":"cap_BfzIt6mN2E0CsWMCX_Qe5","slug":"black-scholes-options-pricer-86e7ae66","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/v1/black-scholes-options-pricer","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_ekKuLi-MFpgPwmoUsWhVT","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":"Computes European call/put fair value and Greeks (delta, gamma, theta, vega, rho) from spot, strike, days-to-expiry, rate, and volatility; optionally solves for implied volatility given a market price.","exampleAgentPrompt":"Price 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 — give me the fair value and all the Greeks.","exampleUseCases":[{"title":"Options fair value for trading desk","prompt":"What's the Black-Scholes fair value and all Greeks for a European put with spot at $320, strike at $310, 60 days to expiry, 4.5% interest rate, and 30% volatility?"},{"title":"Implied volatility extraction from market price","prompt":"I see a call option trading at $8.50 in the market — spot is $200, strike is $205, 21 days to expiry, and the risk-free rate is 5%. Can you back out the implied volatility for me?"},{"title":"Theta decay check before earnings","prompt":"Calculate the daily theta decay on a European call with spot $100, strike $105, 7 days to expiry, 5% rate, and 40% volatility — I want to know how much time value I'm losing per day."}],"resultDescription":"Returns the option's fair value (theoretical price), plus the five standard Greeks: delta (price sensitivity to spot), gamma (delta sensitivity to spot), theta (time decay per day), vega (sensitivity to volatility), and rho (sensitivity to interest rate). If a market_price is supplied, also returns the implied volatility solved iteratively to match that market price.","failureModes":["Missing required parameters (spot, strike, days-to-expiry, rate, or volatility) return a 400 validation error","Volatility or rate supplied as zero or negative may cause numerical instability or division errors","Implied vol solve may fail to converge if the market_price is outside arbitrage bounds (e.g. below intrinsic value or above spot)","Very short days-to-expiry (near zero) can produce extreme Greeks values","Invalid option type string (not 'call' or 'put') returns a parameter error"],"whenToPreferThis":"Use this endpoint when you need a fast, server-side Black-Scholes calculation without running your own math library — particularly useful in agent workflows that need option fair value or Greeks on demand, or when you want implied volatility solved from a live market price without implementing Newton-Raphson yourself. Prefer this over general-purpose computation endpoints because it handles all five Greeks and IV solve in a single call.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-16T01:05:13.666Z","isFirstParty":false}