{"uid":"cap__QxijYNmZcjD0kXjNYix5","slug":"black-scholes-d1-d2-calculator-501570d2","name":"Black-Scholes d1 d2 Calculator","description":"Compute Black-Scholes d1 and d2 from spot/strike/vol/time/rate. Call when you need BS inputs for Greeks without a market feed. Returns d1 and d2 as deterministic JSON for $0.001 USDC via x402 on Base. First-party local math only—no RPC, live market feed, API keys, storage, or mediagen. Advisory only; the caller owns capital, risk, and production controls.","url":"https://api.delx.ai/api/v1/x402/bs-d1-d2","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_IUbwIN6DBgA57ZJAC4MiY","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 d1 and d2 intermediate values from spot price, strike price, volatility, time to expiry, and risk-free rate","exampleAgentPrompt":"Calculate Black-Scholes d1 and d2 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 prep without market feed","prompt":"I need d1 and d2 for a call option where the underlying is trading at 150, strike is 155, implied vol is 25%, time to expiry is 0.5 years, and the risk-free rate is 4.5% — I'm about to compute my delta hedge ratio."},{"title":"Greeks calculation for options inventory","prompt":"Give me the Black-Scholes d1 and d2 values for an option with spot 200, strike 190, vol 30%, 0.1 years to expiry, and zero risk-free rate — I need these as inputs for my Greeks engine."},{"title":"Options pricing model validation","prompt":"Can you compute d1 and d2 using spot 50, strike 50, volatility 15%, time to expiry 1 year, and risk-free rate 2%? I want to cross-check my own implementation of the Black-Scholes formula."}],"resultDescription":"Returns a deterministic JSON object containing the computed d1 and d2 scalar values derived from the Black-Scholes formula, given the provided spot price, strike price, volatility, time to expiry, and risk-free rate. No market data is fetched; computation is purely local math.","failureModes":["Invalid input: spot or strike <= 0 returns error","Invalid input: vol <= 0 returns error","Invalid input: t_years <= 0 returns error","Missing required fields returns validation error","Payment failure: insufficient USDC balance or x402 protocol error"],"whenToPreferThis":"Choose this endpoint when you need deterministic, purely local Black-Scholes d1 and d2 values with no dependency on live market data, API keys, or external feeds. Ideal for options Greeks pipelines that supply their own spot/vol/rate inputs and need a reliable, cheap, stateless math primitive. Prefer over rolling your own implementation when you want a verified, auditable result at $0.001 USDC per call.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T01:20:00.982Z","isFirstParty":false}