{"uid":"cap_Z1tM0KqCNRbxq2Uax5gBJ","slug":"api-quantoracle-dev-b2fb9bf5","name":"QuantOracle Options Pricer","description":"QuantOracle: options/price","url":"https://api.quantoracle.dev/v1/options/price","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"K":{"type":"number","title":"K","description":"Strike price","exclusiveMinimum":0},"S":{"type":"number","title":"S","description":"Spot price of the underlying asset","exclusiveMinimum":0},"T":{"type":"number","title":"T","description":"Time to expiration in years","exclusiveMinimum":0},"q":{"type":"number","title":"Q","default":0,"description":"Continuous dividend yield"},"r":{"type":"number","title":"R","default":0.05,"description":"Risk-free interest rate (annualized)"},"type":{"enum":["call","put"],"type":"string","title":"Type","default":"call","description":"Option type"},"sigma":{"type":"number","title":"Sigma","description":"Volatility (annualized, e.g. 0.2 = 20%)","exclusiveMinimum":0}}},"responseSchema":null,"example":{"request":{"K":155,"S":150,"T":0.25,"r":0.05,"type":"call","sigma":0.2},"response":{"d1":-0.152898,"d2":-0.252898,"ms":71.16,"_meta":{"url":"https://quantoracle.dev","docs":"https://api.quantoracle.dev/docs","calculator":"https://quantoracle.dev/black-scholes-calculator","powered_by":"QuantOracle"},"price":4.6295,"greeks":{"rho":0.153141,"vega":0.29573,"charm":-0.00108655,"delta":0.439239,"gamma":0.026287,"speed":0.0000927,"theta":-0.0408,"vanna":0.00498597,"volga":0.05717592},"prob_itm":0.4002,"breakeven":159.6295,"intrinsic":0,"live_data":{"note":"Priced with the sigma you supplied. For crypto underlyings, fetch fresh realized vol ($0.01) or perp funding ($0.005) instead of static inputs.","funding":"/v1/live/funding-rates","volatility":"/v1/live/volatility"},"time_value":4.6295}},"exampleRequest":{"K":155,"S":150,"T":0.25,"r":0.05,"type":"call","sigma":0.2},"tags":["x402"],"displayCostAmount":"0.005","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":"$0.005/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.005","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.005","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_aS8ly-UgGehddXA0IZAp-","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.005","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Prices European options using Black-Scholes and returns the full Greeks suite, breakeven, intrinsic/time value, and probability ITM","exampleAgentPrompt":"Price a call option where the underlying is trading at $150, the strike is $155, time to expiration is 3 months (0.25 years), implied vol is 20%, and the risk-free rate is 5% — give me the full Greeks including delta, gamma, theta, vega, and the probability it expires in the money.","exampleUseCases":null,"resultDescription":"Returns option fair value (price), d1/d2 intermediates, full Greeks suite (delta, gamma, theta, vega, rho, vanna, volga, charm, speed), probability ITM, breakeven price, intrinsic value, time value, and server computation time in milliseconds.","failureModes":["Missing required parameters (K, S, T, r, sigma, type) returns validation error","T <= 0 (expired option) may cause mathematical singularity","Negative sigma or sigma = 0 causes division-by-zero in Black-Scholes","Invalid option type (not 'call' or 'put') returns 400 bad request","Extremely deep ITM or OTM values may produce near-zero Greeks with floating point precision limits","Payment failure or insufficient USDC balance returns 402 payment required"],"whenToPreferThis":"Choose this endpoint when you need fast, precise Black-Scholes pricing with the complete second-order Greeks suite (vanna, volga, charm, speed) in a single call. Ideal for options pricing engines, risk dashboards, trading bots, or educational tools that require more than just price — especially when you want probability ITM and breakeven alongside Greeks. Prefer over generic financial APIs when you need the full analytical package at low cost per call.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T06:34:12.517Z","isFirstParty":false}