What the calculator computes
Black-76 is the standard model for options on futures and forwards. It prices a call and a put from five inputs: the futures price, the strike, the time to expiry, the risk-free rate and an implied volatility. The calculator takes time to expiry as the number of calendar days between your valuation date and the expiry, divided by 365, so changing the valuation date changes the result even if nothing else moves.
Because the model is built around a forward price, enter the futures price for the contract month rather than an unrelated spot value. The default risk-free rate in the calculator is 7.45%; use 0 if you want a zero-rate calculation. Underlying, strike and volatility must be positive, and the expiry must fall after the valuation date.
Black-76 treats the options as European (exercisable only at expiry) and assumes one constant volatility. Real option chains show a different implied volatility at every strike, so a single volatility input is a simplification.
Price a contract in six steps
- Select the symbol and expiry. The page fills in the contract's underlying price and its listed strikes.
- Confirm the valuation date. Time to expiry is counted in calendar days from this date, so pricing next week's value needs next week's date.
- Check the futures price. Edit it if you want to price a hypothetical level instead of the loaded one.
- Choose a strike, either from the strike list or by typing one.
- Enter the implied volatility for that strike and expiry, plus the risk-free rate.
- Select Price options, then read the call and put premiums, the Greeks and the nine-cell scenario table.
Reading the outputs
| Output | What it estimates | How to use it |
|---|---|---|
| Call and put premium | The model's theoretical value of each option. | Compare with live bid, ask and last price. A gap can reflect a different volatility, rate, forward price or day-count, not only mispricing. |
| Delta | Change in premium for a small move in the futures price. | Roughly the sensitivity of the position; calls are positive and puts are negative. |
| Gamma | How quickly delta changes as the futures price moves. | Highest near the money and close to expiry. The call and put share the same gamma. |
| Vega | Change in premium for a change in volatility. | Shared by the call and put. As written in the model, it is the change per 1.00 (100 percentage points) of volatility; divide by 100 for an approximate per-point value. |
| Theta | Change in premium as time passes, other inputs fixed. | As written, an annual figure. Divide by 365 for an approximate per-day value. |
| Rho | Sensitivity to the interest rate. | Usually minor for short-dated options and larger for longer expiries. |
Because vega and theta are shown as model derivatives, check their units against your broker platform before comparing numbers side by side.
The nine-cell scenario table
Below the results, the calculator re-prices the same strike and expiry for every combination of three futures-price moves (-5%, no change and +5%) and three volatility changes (-20%, no change and +20% of the entered volatility). Volatility shifts are relative: 16% volatility shifted by +20% becomes 19.2%, not 36%.
The table is more informative than any single Greek because the effects interact. A large price move changes how much volatility matters, and a volatility change matters most when the strike is near the money.
Worked example: an at-the-money contract
Take an illustrative futures price and strike of 22,500, 30 calendar days to expiry, 16% volatility and a 7.45% rate. With the futures price equal to the strike, the model gives the same value for the call and the put, about 409.19 each. Call delta is about 0.51 and put delta about -0.49. Raw vega is about 2,557 (roughly 25.6 per volatility point) and call theta is about -2,519 a year (roughly -6.9 a day).
| Futures price move | Volatility change | Call value | Put value |
|---|---|---|---|
| -5% | 0% | 66.2 | 1,184.3 |
| 0% | -20% (to 12.8%) | 327.4 | 327.4 |
| 0% | +20% (to 19.2%) | 491.0 | 491.0 |
| +5% | 0% | 1,195.6 | 77.5 |
Illustrative arithmetic only; these are not current quotes. A 5% move in the futures price changes the call by far more than a 20% change in volatility here, which is typical for a 30-day, near-the-money option.
What a model value cannot tell you
A theoretical premium is a benchmark, not a price you can trade. Bid-ask spreads, liquidity, skew, discrete price jumps and exchange conventions all push live premiums away from the model. Greeks are local estimates: they describe a small move with everything else fixed, and real profit and loss is nonlinear when price, volatility and time change together.
Use the calculator to ask better questions, such as which strikes are sensitive to volatility, or what a position could look like after a 5% move, and then check the answer against live quotes in the option chain and the Greeks guide.