Basics

Time Value and Greeks

Option price = intrinsic value + time value. Time value decays into expiration.

Price logic

What is inside the price

The option price = intrinsic value + time value. Time value gets smaller as the option approaches expiration. That is reflected by theta.

Premium 8 EUR, spot 105, strike 100: 5 EUR intrinsic value and 3 EUR time value.

8 EUR option price = 5 EUR + 3 EUR

5 EURIntrinsic value3 EURTime value

Long call: spot 105 EUR, strike 100 EUR. Intrinsic value = max(105 − 100, 0). Time value = 8 − 5. Bar widths match the components of the option price.

Greeks

The four key Greeks

Delta Reaction to the price move
Theta How much time value does the option lose per day?
Time value declines; daily decay accelerates

90 DTE: 5.94 EUR30 DTE: 3.43 EUR0 DTE: 0 EUR
- ATM time value
Model of an option held at ATM: spot = strike = 100 EUR, IV 30%, starting at 90 DTE; zero rates and dividends. This curve shows remaining time value, not theta itself. Theta is the daily change: about −0.02 EUR at 90 DTE and −0.06 EUR at 10 DTE. Price and IV changes alter the actual path.
Time decay depends strongly on moneyness: ATM options often decay fastest near expiration, ITM options tend to decay more evenly, and OTM options consist only of time value that falls to zero by expiration.
Gamma Change in delta
Vega Reaction to IV
Example Delta 0.45 means: +1 EUR in the underlying = roughly +0.45 EUR in the option.