{"uid":"cap_LLYihkPxMxB9oOxixtIAe","slug":"agent402-uk-black-scholes-options-pricer-123f6531","name":"Agent402 UK Black-Scholes Options Pricer","description":"Don't burn tokens on deterministic work. Go/no-go jobs first: payout preflight, text firewall (PII/secrets), budget check — then rails, calendars, finmath. x402 USDC on Base. UK + global. agent402.co.uk — not agent402.tools. $0.001–$0.002 USDC on Base. No API keys.","url":"https://agent402.co.uk/v1/math/black-scholes?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"K":{"type":"number","description":"Strike"},"S":{"type":"number","description":"Spot"},"T":{"type":"number","description":"Years to expiry"},"r":{"type":"number","description":"Risk-free rate"},"type":{"type":"string","description":"call | put"},"sigma":{"type":"number","description":"Volatility"}}},"responseSchema":{"type":"json","example":{"type":"call","price":10.45058357218556,"greeks":{"delta":0.6368306511756191,"gamma":0.0187620173458469}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.002","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":"down","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_YOiRonovBvqhMSdJiOWlq","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":"Computes exact closed-form Black-Scholes price and Greeks (delta, gamma) for a European call or put option given spot, strike, time to expiry, risk-free rate, and volatility.","exampleAgentPrompt":"Price a call option using Black-Scholes where the spot is $150, strike is $155, time to expiry is 0.5 years, risk-free rate is 5%, and implied volatility is 20%.","exampleUseCases":[{"title":"Delta-hedge ratio for a put","prompt":"I need the exact Black-Scholes price and delta for a put option: spot is $200, strike is $195, 0.25 years to expiry, risk-free rate 4.5%, and vol of 25%. Give me the closed-form result, not an LLM estimate."},{"title":"Pre-trade option fair value check","prompt":"Before I place this trade, can you compute the Black-Scholes fair value of a call option — spot $3500, strike $3600, 90 days to expiry (that's 0.247 years), risk-free rate 5.25%, volatility 18%?"},{"title":"Gamma risk assessment at earnings","prompt":"What's the gamma on a call option with spot $80, strike $80, 1 week to expiry (0.019 years), rate 5%, and implied vol spiked to 60%? I want the exact Black-Scholes number to assess pin risk."}],"resultDescription":"Returns a JSON object containing the option type ('call' or 'put'), the exact closed-form Black-Scholes theoretical price, and Greeks including delta (sensitivity of price to spot) and gamma (rate of change of delta). Example: {type: 'call', price: 10.45, greeks: {delta: 0.637, gamma: 0.019}}.","failureModes":["Missing required inputs (S, K, T, r, sigma) — likely returns 400 or validation error","Negative time to expiry (T ≤ 0) — mathematically undefined, may return error or NaN","Sigma of zero — results in degenerate pricing (deep ITM/OTM binary outcome); may error","Incorrect option type string (not 'call' or 'put') — likely returns validation error","Payment failure (x402 protocol) — 402 Payment Required if USDC payment not attached"],"whenToPreferThis":"Prefer this endpoint whenever an AI agent needs mathematically exact Black-Scholes option pricing and Greeks rather than an LLM approximation. Ideal for quant workflows, delta-hedging calculations, pre-trade fair value checks, risk management, and any scenario where numerical precision matters. Use over LLM estimation whenever S, K, T, r, and sigma are all known quantities.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-12T23:27:42.186Z","isFirstParty":false,"canonicalSlug":"agent402-uk-black-scholes-options-pricer-123f6531"}