Model and input conventions
Enter annual volatility, the continuously compounded annual funding rate and the underlying yield in percentage units: 20 means 20%. Time uses calendar days divided by 365. The implementation discounts the underlying by its yield and the strike by the funding rate, then applies the normal cumulative distribution to the Black–Scholes terms. Vega and rho are scaled to a one-percentage-point move; theta measures a calendar day passing.
Worked numerical example
With spot and strike both 100, 365 days remaining, a 5% rate, zero yield and 20% volatility, the model call is approximately 10.450584 and the put is 5.573526. Call delta is approximately 0.636831. Vega is approximately 0.375240 quote units for one volatility percentage point, so a very small change from 20% toward 21% initially raises value at roughly that rate.
Read the scenario table
The spot-scenario rows reprice both options after changing only the underlying price. Each row retains the original maturity and volatility assumptions; it is not an expiry payoff or a forecast of tomorrow’s quote. Compare the delta columns to see how first-order exposure changes across the chosen price range. For an expiry-only strategy diagram, use the dedicated payoff calculators instead.
Where the model stops
This is a European diffusion model with constant rates, yield and volatility. It excludes jumps, changing volatility skew, transaction costs and early exercise. At expiry or zero volatility it reports deterministic payoff values but leaves Greeks undefined. Inverse or coin-settled exchange options may require a different numeraire, delivery process or conversion; their displayed premiums cannot automatically be entered as USD premiums.