BEHIND THE NUMBERS
How this calculation works
Worked example
For S = K = £100, one year, 20% volatility and a 5% continuously compounded rate with no dividends, the standard analytical benchmark is call £10.45058357 and put £5.57352602 per unit.
Example result: £10.45
Continuous yield needs its own discount factor
Dividend yield changes both the forward relationship and the present value of the underlying. Merely subtracting it from the interest rate without discounting the spot component would not implement the dividend-adjusted model.
Premium per unit and per contract
The headline is the premium for one underlying unit. The contract result multiplies by the units you enter; contract sizes vary, so no exchange’s contract specification is assumed.
Assumptions and rounding
- European exercise, constant volatility, constant continuous rates and a continuous proportional dividend yield.
- Prices are displayed to pennies, without intermediate rounding. The normal-distribution calculation uses the numerical methods cited below.
Questions about this calculator
Can I price an American option?
No. The model does not value the right to exercise before expiry. Use a model that implements early exercise for that contract.
What does vega mean here?
It is the approximate price change per underlying unit for a one percentage-point increase in annual volatility, with the other inputs fixed.