{"uid":"cap_5qlDl2mfn8Xa-fcH1AKXp","slug":"delx-commerce-black-scholes-delta-calculator-a2fb7628","name":"Delx Commerce — Black-Scholes Delta Calculator","description":"Pay-per-result APIs for agents. No signup. Exact price. Verifiable delivery. USDC on Base + Solana via x402.","url":"https://commerce.delx.ai/api/v1/x402/bs-delta?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"vol":{"type":"number","description":"Annualized volatility as decimal (>0), e.g. 0.2 = 20%"},"rate":{"type":"number","description":"Risk-free rate as decimal (optional, default 0)"},"spot":{"type":"number","description":"Underlying spot price (>0)"},"strike":{"type":"number","description":"Option strike price (>0)"},"t_years":{"type":"number","description":"Time to expiry in years (>0)"}}},"responseSchema":{"type":"json","example":{"schema":"delx/util-bs-delta/v1","delta_put":-0.4800611941616275,"delta_call":0.5199388058383725}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.001","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":"$0.001/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.001","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.001","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_guzR6UPLTRk5UskH61JlA","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.001","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes Black-Scholes delta (call and put) for an option given spot, strike, volatility, time to expiry, and risk-free rate","exampleAgentPrompt":"What's the call and put delta for an option with a spot price of 100, strike of 105, annualized volatility of 20%, 0.25 years to expiry, and a risk-free rate of 5%?","exampleUseCases":[{"title":"Delta hedging position sizing","prompt":"I need to hedge my equity options book — can you calculate the call and put delta for an option with spot at 4500, strike at 4600, vol of 18%, 45 days to expiry (0.123 years), and a risk-free rate of 4.5%?"},{"title":"At-the-money option sensitivity check","prompt":"What's the Black-Scholes delta for an ATM call and put where spot equals strike at 250, annualized vol is 30%, time to expiry is 0.5 years, and the risk-free rate is 0?"},{"title":"Options trading strategy evaluation","prompt":"I'm evaluating a covered call strategy — compute the call delta for a stock trading at 50 with a strike of 55, implied vol of 25%, 60 days to expiry (0.164 years), and a risk-free rate of 3%."}],"resultDescription":"Returns a JSON object with schema identifier 'delx/util-bs-delta/v1', containing delta_call (positive float between 0 and 1 representing call option delta) and delta_put (negative float between -1 and 0 representing put option delta), computed using the Black-Scholes model.","failureModes":["Missing required fields (spot, strike, vol, t_years) returns a validation error","vol <= 0 or spot <= 0 or strike <= 0 causes invalid input error","t_years <= 0 (expired option) causes invalid input error","Payment failure via x402 if USDC balance is insufficient or transaction is rejected"],"whenToPreferThis":"Choose this endpoint when you need a fast, pay-per-call Black-Scholes delta computation without API key signup, especially in agentic workflows where micropayments via USDC (x402 protocol) are acceptable. Ideal for one-off or low-volume options greek calculations where subscribing to a full financial data service is overkill.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-01T00:53:50.007Z","isFirstParty":false,"canonicalSlug":"delx-commerce-black-scholes-delta-calculator-a2fb7628"}