{"uid":"cap_xjKcUW6flzBVnDjs4S0wm","slug":"delx-commerce-black-scholes-d1-and-d2-calculator-1dd0dcbf","name":"Delx Commerce — Black-Scholes d1 and d2 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-d1-d2?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":{"d1":0.05000000000000001,"d2":-0.05,"schema":"delx/util-bs-d1-d2/v1"}},"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_zmACmkFwDOebxpCuDNRQe","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 the Black-Scholes d1 and d2 intermediate values for an option given spot price, strike, volatility, time to expiry, and risk-free rate.","exampleAgentPrompt":"Calculate the Black-Scholes d1 and d2 for an option with a spot price of 100, strike of 105, annualized volatility of 20%, time to expiry of 0.5 years, and a risk-free rate of 5%.","exampleUseCases":[{"title":"Option delta computation for a trading bot","prompt":"I need d1 and d2 for a call option — spot is 150, strike is 155, vol is 25%, it expires in 90 days (0.247 years), and the risk-free rate is 4.5%. I want to feed these into a delta calculation."},{"title":"At-the-money option pricing check","prompt":"What are the Black-Scholes d1 and d2 values for an at-the-money option where spot and strike are both 200, volatility is 30%, time to expiry is 1 year, and the risk-free rate is zero?"},{"title":"Implied probability analysis for a short-dated option","prompt":"Give me d1 and d2 for a short-dated option: spot 50, strike 52, annualized vol 18%, expires in 2 weeks (0.038 years), risk-free rate 5%."}],"resultDescription":"A JSON object containing the computed d1 and d2 scalar values (both as floating-point numbers), along with a schema identifier string ('delx/util-bs-d1-d2/v1') confirming the response format.","failureModes":["Missing or zero/negative spot or strike price returns a validation error","Zero or negative time to expiry causes a math domain error","Zero or negative volatility is invalid and will be rejected","Non-numeric inputs return a 400 bad request","Payment not provided or insufficient USDC results in a 402 Payment Required response"],"whenToPreferThis":"Choose this endpoint when you need a reliable, pay-per-call micro-service to compute the Black-Scholes d1/d2 intermediates without managing any subscription or API key. It is ideal for AI agents or trading pipelines that need on-demand options math at minimal cost ($0.001 USDC per call) with verifiable USDC settlement on Base or Solana via x402.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-01T00:54:02.483Z","isFirstParty":false,"canonicalSlug":"delx-commerce-black-scholes-d1-and-d2-calculator-1dd0dcbf"}