{"uid":"cap_jGXeaXxzgIY9sDJS-W8Pc","slug":"hermes-plant-black-scholes-option-pricing-greeks-c55587f6","name":"Hermes Plant Black-Scholes Option Pricing & Greeks","description":"Deterministic Black-Scholes-Merton European option pricing and Greeks. Returns price, d1/d2, full Greeks (delta, gamma, vega, theta, rho) in canonical and conventional display units (vega per 1%, theta per day, rho per 1%), plus intrinsic value, time value, and moneyness. Supports continuous dividend yield. Pure math from caller-supplied parameters — no market-data feed, no fabrication.","url":"https://hermesplant.com/api/agent-services/options/price","method":"GET","headers":{},"bodySchema":{"type":"object","properties":{"spot":{"type":"number","description":"Current price of the underlying (> 0)."},"strike":{"type":"number","description":"Option strike price (> 0)."},"optionType":{"type":"string","description":"'call' or 'put' (default 'call')."},"volatility":{"type":"number","description":"Annualized volatility (sigma) as a fraction, e.g. 0.2 for 20%."},"riskFreeRate":{"type":"number","description":"Annual continuously-compounded risk-free rate, e.g. 0.05 (default 0)."},"timeToExpiry":{"type":"number","description":"Time to expiry in years (e.g. 0.5 = 6 months)."},"dividendYield":{"type":"number","description":"Annual continuous dividend yield, e.g. 0.02 (default 0)."}}},"responseSchema":{"type":"json","example":{"d1":0.35,"d2":0.15,"price":10.450576,"greeks":{"rho":53.232483,"vega":37.524035,"delta":0.636831,"gamma":0.018762,"theta":-6.414028,"rhoPer1Pct":0.532325,"thetaPerDay":-0.017573,"vegaPer1Pct":0.37524},"service":"optionlens","findings":[{"fix":null,"why":"Black-Scholes-Merton valuation summary.","rule":"valuation","evidence":"price=10.4506 d1=0.35 d2=0.15 moneyness=at-the-money","severity":"info"}],"moneyness":"at-the-money","requestId":"opt-db556a1a","timeValue":10.450576,"optionType":"call","intrinsicValue":0}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.25","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":"$0.25/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.25","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.25","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_7K8lm0M0avF_uwqGg5yaz","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.25","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes Black-Scholes-Merton option price along with full Greeks (delta, gamma, theta, vega, rho) for a given options contract, paid per call via x402.","exampleAgentPrompt":"Price a European call option where the underlying is at $100, strike is $100, time to expiration is 1 year, risk-free rate is 5%, and implied volatility is 20% — give me the full Greeks including delta, gamma, theta, vega, and rho.","exampleUseCases":[{"title":"Greeks breakdown for options risk management","prompt":"I'm managing a portfolio of equity options and need a full Greeks breakdown for a put option on a stock trading at $150 with a $155 strike, 45 days to expiration, 4% risk-free rate, and 30% implied volatility — give me delta, gamma, theta, vega, and rho so I can assess my exposure."},{"title":"Fair value check before executing trade","prompt":"Before I pull the trigger on buying this call option, can you run a Black-Scholes valuation for me? The underlying is at $250, strike is $260, there are 90 days left to expiration, risk-free rate is 5.25%, and implied vol is 25% — I want the theoretical price, moneyness classification, and all the Greeks."},{"title":"Automated options pricing in trading workflow","prompt":"As part of my autonomous trading workflow, price a European put where the stock is at $80, strike is $75, time to expiration is 6 months, risk-free rate is 4.5%, and implied volatility is 18% — return the full Greeks bundle and intrinsic versus time value split so the system can decide whether to execute."}],"resultDescription":"Returns the theoretical option price, d1 and d2 intermediate values, moneyness classification (at-the-money/in-the-money/out-of-the-money), intrinsic value, time value, and a complete Greeks bundle (delta, gamma, theta, vega, rho, plus per-1% and per-day convenience scalings), along with a valuation findings summary and a unique requestId.","failureModes":["Missing required input parameters (underlying price, strike, expiry, volatility, rate) returns a 4xx validation error","Negative or zero volatility input may cause mathematical errors or rejection","Extremely short time-to-expiry values may produce degenerate Greeks","Insufficient USDC balance or failed x402 payment returns a payment-required error","Network timeout if the service is temporarily unavailable"],"whenToPreferThis":"Choose this endpoint when an AI agent needs fast, deterministic, test-backed Black-Scholes option pricing with a full Greeks output in a single call, especially in autonomous trading or risk workflows that require pay-per-call metering via x402. Prefer over in-house implementations when auditability, structured findings output, and deterministic test-backed results matter.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T18:39:58.078Z","isFirstParty":false}