Theta

Theta measures how much an option loses in value with the passage of one day, holding everything else constant. It is the price of time, and it is almost always working against the buyer.

Theta = change in option price / one day passing (usually negative for buyers)

A worked example

Own a call, premium 4.00, theta -0.05.
If nothing else changes, tomorrow it is worth ~ 3.95,
the day after ~ 3.90, and so on.

That bleed is the extrinsic (time) value decaying toward zero. At expiry, only intrinsic value remains.

Decay is not linear

Time decay accelerates as expiry approaches. An option loses time value slowly when months remain and rapidly in the final weeks — the curve steepens sharply near the end. ATM options decay fastest of all.

The two sides of theta

• Buyers are short theta — every day that the underlying does not move enough, they lose. Being right about direction but too slow still loses money.
• Sellers are long theta — they collect decay each day the market sits still. This is the appeal of selling premium.

The honest trade-off

Theta and gamma pull in opposite directions. Sellers earn theta but carry the dangerous short-gamma risk from the previous lesson; buyers pay theta but get the protective positive gamma. You cannot have the daily income without the tail risk — that is the fundamental bargain of options.