{"uid":"cap_MOBeWMVydiACcSsf6KbiM","slug":"finmath-black-scholes-option-pricer-11fa05d1","name":"finmath Black-Scholes Option Pricer","description":"Deterministic finance and crypto math for AI agents: TradFi (NPV, IRR, XIRR, Black-Scholes + Greeks, bonds, VaR, Sharpe) and DeFi (impermanent loss, perp liquidation, funding, Uniswap v3, health factor, cost basis). Exact, model-free arithmetic that LLMs get wrong — priced per call in USDC.","url":"https://finmath.qzqh5rrbkz.workers.dev/v1/black_scholes_option","method":"POST","headers":{},"bodySchema":{"type":"object","required":["rate","spot","strike","time_years","volatility"],"properties":{"kind":{"type":"string","description":"kind"},"rate":{"type":"number","description":"rate"},"spot":{"type":"number","description":"spot"},"strike":{"type":"number","description":"strike"},"time_years":{"type":"number","description":"time_years"},"volatility":{"type":"number","description":"volatility"}}},"responseSchema":{"type":"object","required":["result","meta"],"properties":{"meta":{"type":"object"},"result":{}}},"example":{"request":{"kind":"call","rate":0.05,"spot":100,"strike":100,"time_years":1,"volatility":0.2},"response":{"meta":{"tool":"black_scholes_option","model":true,"disclaimer":"Deterministic calculation utility. Not financial, investment, or trading advice.","assumptions":["European exercise","no dividend yield","constant volatility and rate"],"deterministic":true},"result":{"d1":0.35000000000000003,"d2":0.15000000000000002,"rho":53.232481545376345,"vega":37.52403469169379,"delta":0.6368306511756191,"gamma":0.018762017345846895,"price":10.450583572185565,"theta":-6.414027546438197}}},"exampleRequest":{"kind":"call","rate":0.05,"spot":100,"strike":100,"time_years":1,"volatility":0.2},"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"settled","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":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_yHjBDfg2fWFBYvSqSScm-","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes Black-Scholes option price and Greeks for a European call or put given spot, strike, rate, volatility, and time to expiry","exampleAgentPrompt":"What's the Black-Scholes price and Greeks for a call option on a stock trading at $150, strike $155, risk-free rate 5%, volatility 25%, expiring in 0.5 years?","exampleUseCases":null,"resultDescription":"Returns a result object with the computed option price and associated Greeks (delta, gamma, theta, vega, rho), plus a meta object with call metadata. Values are exact arithmetic outputs, not LLM estimates.","failureModes":["Missing required fields (rate, spot, strike, time_years, volatility) returns a 400-level error","Negative time_years or volatility may produce undefined/error result","Invalid option kind string may default to call or return an error","Payment not included or rejected returns HTTP 402"],"whenToPreferThis":"Use this endpoint when you need exact, deterministic Black-Scholes pricing and Greeks rather than relying on an LLM's approximate arithmetic. Prefer it over general-purpose math tools when the task is specifically European option pricing with standard inputs and you need trustworthy numerical output for trading, risk, or educational purposes.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T18:55:16.798Z","isFirstParty":false}