Black-Scholes Option Calculator
OPTIONS · PRICE & GREEKS · LIVE DERIBIT CHECK OR MANUAL INPUTS
Theoretical option price and Greeks from Black-Scholes — manual inputs, or checked live against a real Deribit BTC/ETH instrument's own quoted price.
Pulls that instrument's own live spot, strike, days to expiry, and implied volatility from Deribit, then checks whether its quoted mark price is consistent with Black-Scholes at that IV.
What is Black-Scholes and why check a real instrument against it?
Black-Scholes is the standard model for theoretically pricing a European option from five inputs: spot, strike, time to expiry, volatility, and the risk-free rate. Deribit's own options are European-style (no early exercise), so the model applies cleanly. This calculator does two things: prices any hypothetical option from manual inputs, or pulls a real Deribit BTC/ETH instrument's own spot/strike/expiry/IV and checks whether its quoted mark price is actually consistent with Black-Scholes at that volatility — a live sanity check, not an estimate.
The formulas
- d1 = [ln(S/K) + (r + σ²/2)T] / (σ√T), d2 = d1 − σ√T
- Call = S·N(d1) − K·e^(−rT)·N(d2)
- Put = K·e^(−rT)·N(−d2) − S·N(−d1)
- Delta(call) = N(d1); Gamma = φ(d1) / (S·σ·√T); Vega = S·φ(d1)·√T
Worked example
Classic textbook case: S=$100, K=$100, r=5%, volatility=20%, 1 year to expiry:
- d1 = 0.35, d2 = 0.15
- Call = $10.4506, Put = $5.5735
- Delta(call) = 0.6368
Coin-denominated price convention
Deribit quotes BTC/ETH option premiums in the underlying coin, not USD. This tool converts the standard USD Black-Scholes price into that convention by dividing by spot — cross-checked live against a real deep-in-the-money Deribit instrument, where this formula's coin price matched Deribit's own quoted mark price to within normal bid-ask noise. Greeks shown here stay standard USD-denominated Black-Scholes Greeks, the universal convention every options calculator uses, rather than a further coin-adjusted variant.
Where to go next
Already decided on a position and just want the payoff at expiry, not today's theoretical price? Use the Options Payoff Calculator. Selling premium against coin you already hold? Try the Covered Call Calculator. Have a price but need the volatility instead of the price? Use the Implied Volatility Calculator.
Use via API or MCP
This calculation is available as a deterministic API call — useful for bots or AI agents that need to price options or check a live quote against the model, not guess.
What does "live mode" actually check?
It fetches a real Deribit BTC/ETH instrument's own spot price, strike, days to expiry, and implied volatility, runs them through Black-Scholes, and compares the result to Deribit's own quoted mark price — a direct, reproducible check of whether the exchange's price is internally consistent, not an AI guess about fair value.
Why is the price shown in coin terms in live mode?
Deribit's BTC/ETH options settle in the underlying coin. This tool converts the standard USD Black-Scholes price by dividing by spot to match that convention, so it lines up with the mark price Deribit itself quotes.
Why does the risk-free rate default to 0%?
Crypto options markets conventionally treat the risk-free rate as negligible — there's no equivalent to a government bond yield embedded in the pricing the way there is for traditional equity options. You can still override it manually.
Are the Greeks coin-denominated too?
No — delta, gamma, theta, vega, and rho are standard USD-denominated Black-Scholes Greeks, the convention every options calculator and textbook uses. Only the price itself gets an additional coin-denominated convenience figure.