What a call is worth before expiry
A call option gives the right to buy a share at a fixed strike price until a fixed date. Its fair value depends on five things — the share price, the strike, time to expiry, volatility and the risk-free rate — and the Black-Scholes model turns those into a price. This calculator runs that model and returns the call, the matching put and the two intermediate figures d₁ and d₂.
The formula
Worked example: share at $100, strike $100, one year, 20% volatility, 5% rate
- d₁ = 0.35, d₂ = 0.15
- Call value: $10.45 — put value: $5.57
An at-the-money call with a year to run is worth about a tenth of the share price at 20% volatility. N(d₁), the delta, is 0.64: the call moves about 64 cents for each dollar the share moves.
What moves the price
| Volatility | Time to expiry | Call value |
|---|---|---|
| 20% | 1 year | $10.45 |
| 30% | 1 year | $14.23 |
| 20% | 6 months | $6.89 |
| 20% | 2 years | $16.13 |
Ten points of volatility add 36% to the price with nothing else changed. Halving the time removes a third of the value, not half — time value decays faster as expiry approaches, which is why the last month costs an option buyer the most.
Put-call parity
The call and put on the same strike and date are tied together: C − P = S − K·e^(−rT). Here 10.45 − 5.57 = 4.88, and 100 − 100 × e^(−0.05) = 4.88. If a market quote breaks this relation, one of the two options is mispriced and the gap can be traded.
Where the model is wrong
Black-Scholes assumes constant volatility and a log-normal share price. Markets price crashes as more likely than that, so real puts far below the market trade above the model's value — the volatility "smile". The model also prices European options, exercisable only at expiry; American-style calls on non-dividend shares are worth the same, but puts and options on dividend payers are not.
The input that matters most, volatility, is the one nobody knows. Traders run the model backwards: from the market price to the implied volatility, and compare that to history.
What this calculator leaves out
Dividends before expiry, which lower a call's value; early exercise; and transaction costs, which on a $10 option can be 5% each way.
Related calculators
- Options spread calculator — combining two strikes
- Futures contract calculator — the other leveraged derivative
- Stock calculator — the underlying position without leverage