{"uid":"cap_PayqAdcSEI5O02xfD2ZOh","slug":"delx-bs-greeks-lite-black-scholes-options-greeks-calculator-93196a83","name":"Delx BS Greeks Lite — Black-Scholes Options Greeks 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-greeks-lite?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":{"vega":0.199221957047382,"delta":0.5199388058383725,"gamma":0.0398443914094764,"schema":"delx/util-bs-greeks-lite/v1","theta_call":-0.02183254323806927}},"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_KNM0XuTEhVU7epDhmqM2p","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 options Greeks (delta, gamma, theta, vega) for a given option using spot price, strike, volatility, time to expiry, and risk-free rate","exampleAgentPrompt":"Calculate the Black-Scholes Greeks for a call 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% — I need delta, gamma, theta, and vega.","exampleUseCases":[{"title":"Hedge ratio calculation for options portfolio","prompt":"I need the delta and gamma for an 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% — I want to figure out my hedge ratio."},{"title":"Theta decay monitoring before expiry","prompt":"Can you tell me the daily theta decay on a call option? Spot is 200, strike is 200, vol is 30%, it expires in 2 weeks (about 0.038 years), and the risk-free rate is 3%."},{"title":"Vega sensitivity for volatility trading","prompt":"I'm trading volatility and need the vega for an option: underlying spot at 50, strike at 48, annualized vol 40%, 90 days to expiry (0.247 years), risk-free rate 0."}],"resultDescription":"Returns a JSON object containing Black-Scholes Greeks: delta (rate of change of option price with respect to spot), gamma (rate of change of delta with respect to spot), vega (sensitivity to volatility), and theta_call (time decay of the call option per year), along with a schema identifier string.","failureModes":["Missing or zero/negative spot price returns validation error","Missing or zero/negative strike price returns validation error","Zero or negative time to expiry (t_years) returns validation error","Zero or negative volatility (vol) returns validation error","Payment failure via x402 protocol results in 402 Payment Required response","Malformed JSON body returns 400 Bad Request"],"whenToPreferThis":"Choose this endpoint when you need a fast, pay-per-call, no-signup Black-Scholes Greeks computation with cryptographic payment via USDC on Base or Solana. Ideal for AI agents that need occasional or burst options analytics without committing to a subscription, or when verifiable on-chain payment is required. Best for single-option Greek calculations rather than bulk portfolio analytics.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-01T00:54:02.003Z","isFirstParty":false,"canonicalSlug":"delx-bs-greeks-lite-black-scholes-options-greeks-calculator-93196a83"}