{"uid":"cap_0bSMHyDAVrFERy8WxpVGn","slug":"derivatives-pricer-implied-volatility-single-premium-660ad0da","name":"Derivatives Pricer — Implied Volatility (Single Premium)","description":"x402-paid Black-Scholes European option pricing, Greeks, IV surfaces, price/scenario on submitted smiles (TV bilinear), portfolio risk, free demo, and MCP. USDC exact on Solana (PayAI) and/or Base (CDP when configured). Receive wallets appear only in HTTP 402, never on free discovery.","url":"https://derivatives-pricer-production.up.railway.app/v1/option/implied-vol?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"rate":{"type":"number","description":"Continuous risk-free rate r"},"strike":{"type":"number","description":"Strike K (> 0)","exclusiveMinimum":0},"premium":{"type":"number","minimum":0,"description":"Observed market premium"},"treeSteps":{"type":"integer","maximum":500,"minimum":50},"expiration":{"type":"string","format":"date-time"},"optionType":{"enum":["call","put"],"type":"string"},"underlying":{"type":"number","description":"Underlying price S (> 0)","exclusiveMinimum":0},"optionStyle":{"enum":["european","american"],"type":"string","default":"european"},"forwardStart":{"type":"string","format":"date-time"},"timeToExpiry":{"type":"number","minimum":0,"description":"Time to expiry in years (xor expiration)"},"dividendYield":{"type":"number","minimum":0,"description":"Continuous yield q (default 0)"}}},"responseSchema":{"type":"json","example":{"model":"black-scholes-merton","greeks":{"rho":53.23248343,"vega":37.52403469,"delta":0.63683059,"gamma":0.01876202,"theta":-6.41402764},"inputs":{"rate":0.05,"strike":100,"premium":10.45057562,"optionType":"call","underlying":100,"optionStyle":"european","timeToExpiry":1,"dividendYield":0},"converged":true,"requestId":"00000000-0000-4000-8000-000000000003","computedAt":"2026-01-01T00:00:00.000Z","impliedVol":0.2,"iterations":12,"modelPrice":10.45057562,"priceError":0,"optionStyle":"european","greeksQuality":"analytic"}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.03","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":"$0.03/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.03","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.03","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_NalJfQtZamIgU08CLc2aR","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.03","costPer":"request","priority":0,"asset":"EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes implied volatility from an observed option premium using Black-Scholes, returning IV, converged model price, price error, and full analytic Greeks.","exampleAgentPrompt":"What's the implied volatility on a European call with underlying at 105, strike 100, premium of 8.50, 6 months to expiry, risk-free rate 5%, and no dividends? Also give me the full Greeks.","exampleUseCases":[{"title":"Trader verifying IV on live quote","prompt":"I'm looking at a European put on a stock trading at 98, strike 100, market premium is 5.20, expiring in 3 months, risk-free rate 4.5%, no dividends — what implied volatility does that premium imply, and what are the Greeks?"},{"title":"Quant model calibration check","prompt":"I need to back out the implied vol from a European call: underlying 200, strike 210, observed premium 12.75, time to expiry 0.25 years, rate 5%, dividend yield 1.5%. Does the model converge and what's the implied vol?"},{"title":"Options educator building example","prompt":"For a textbook example, solve for the implied volatility of an at-the-money European call where underlying equals strike at 100, market premium is 10.45, one year to expiry, 5% risk-free rate, and zero dividends — and show me all the Greeks too."}],"resultDescription":"Returns a JSON object with the computed implied volatility (as a decimal, e.g. 0.20 = 20%), whether the Newton-Raphson solver converged, the number of iterations taken, the Black-Scholes model price at that IV, the price error versus the input premium, the five analytic Greeks (delta, gamma, theta, vega, rho), a mirror of the original inputs, a requestId, and a timestamp.","failureModes":["Non-convergence: if the premium is outside the no-arbitrage bounds or the solver cannot converge within its iteration limit, 'converged' will be false and impliedVol may be null or unreliable","Invalid inputs: strike or underlying <= 0 returns a 400-level validation error","Negative premium or premium exceeding intrinsic value causes solver divergence","Very short or zero timeToExpiry can cause numerical instability in vega and thus IV solver failure","Payment failure: if the x402 USDC micropayment on Solana or Base is not completed, the request is rejected with a 402 Payment Required"],"whenToPreferThis":"Choose this endpoint when you need to invert an observed market premium to its implied volatility under Black-Scholes for a European option, especially when you also need analytic Greeks in the same call. Prefer it over a full options chain or surface endpoint when you have a single premium observation. Because it requires no API keys and charges a flat $0.03 USDC per call via x402, it is ideal for agent workflows needing on-demand, pay-per-use IV computation without credential management.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-11T12:35:53.136Z","isFirstParty":false,"canonicalSlug":"derivatives-pricer-implied-volatility-single-premium-660ad0da"}