{"uid":"cap_3m1Ci6tuAsc91819PKBZ6","slug":"black-scholes-option-pricer-greeks-calculator-3d018356","name":"Black-Scholes Option Pricer & Greeks Calculator","description":"Black-Scholes option price and Greeks (delta, gamma, vega, theta) from JSON keys spot, strike, tau (years; 3-month = 0.25), sigma (annualized volatility), and is_call (boolean). Pure closed-form calculation, no market data looked up or stored. vega is ∂price/∂sigma per 1.0 volatility (not per 1%).","url":"https://api.edifiedlab.com/v1/market/black-scholes","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"tau":{"type":"number","minimum":0,"description":"time to expiry in years (3-month = 0.25)"},"rate":{"type":"number","default":0,"description":"annualized risk-free rate (optional; default 0)"},"spot":{"type":"number","exclusiveMinimum":0},"sigma":{"type":"number","minimum":0,"description":"annualized volatility"},"strike":{"type":"number","exclusiveMinimum":0},"is_call":{"type":"boolean","description":"true for a call, false for a put"}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.011","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":"$0.011/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.011","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.011","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_VPZFxpSayrMjUF0LGHpvr","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.011","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes Black-Scholes option price and Greeks (delta, gamma, vega, theta) for European calls or puts given spot, strike, time-to-expiry, and volatility","exampleAgentPrompt":"What's the Black-Scholes price and Greeks for a call option where the stock is trading at $150, the strike is $155, it expires in 3 months, annualized vol is 25%, and the risk-free rate is 4%?","exampleUseCases":[{"title":"Options hedging delta calculation","prompt":"I'm delta-hedging a put option on a stock currently at $200 with a $195 strike, 6 months to expiry, and implied volatility of 30% — can you give me the Black-Scholes delta and gamma so I know how many shares to hold?"},{"title":"Options strategy P&L estimation","prompt":"I want to price a covered call — the underlying is at $50, strike $55, 45 days to expiration (so about 0.123 years), and implied vol is 20% with a 5% risk-free rate. What's the call premium and theta decay per day?"},{"title":"Automated options screener pricing","prompt":"Run a Black-Scholes calculation for a put option: spot $3200, strike $3100, time to expiry 0.5 years, volatility 18%, risk-free rate 3.5% — I need price, delta, and vega for my options screener."}],"resultDescription":"Returns the theoretical option price and the four primary Greeks: delta (∂price/∂spot), gamma (∂²price/∂spot²), vega (∂price/∂sigma per 1.0 volatility unit, not per 1%), and theta (∂price/∂time). All values are derived purely from the closed-form Black-Scholes formula with no market data fetched or stored.","failureModes":["Missing required fields (spot, strike, tau, sigma, is_call) returns a 4xx validation error","Non-positive spot or strike values rejected due to exclusiveMinimum:0 constraint","Negative tau or sigma values rejected due to minimum:0 constraint","Extreme inputs (very deep in/out of the money, near-zero tau) may produce numerically degenerate Greeks such as near-zero vega or very large gamma","Payment failure (insufficient USDC balance) via x402 protocol returns 402 status before computation"],"whenToPreferThis":"Choose this endpoint when you need a fast, pure closed-form Black-Scholes computation with no dependency on live market data — ideal for options pricing bots, hedging calculators, or backtesting pipelines where you already have your own spot price and volatility inputs. Prefer this over broker APIs when you want a lightweight, deterministic calculation without authentication overhead or market-data subscriptions. Note that vega is returned per 1.0 volatility unit (not per 1%), so divide by 100 if you need per-1%-vol sensitivity.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-19T06:33:01.923Z","isFirstParty":false}