In options analysis, what does the option sensitivity measure 'Theta' quantify, and how does it affect option buyers versus option sellers?

[ A ]Theta measures the option's sensitivity to central bank interest rate changes.

[ B ]Theta measures the exact default probability of the underlying company.

[ C ]Theta measures the rate of decline in the option's time value per day as expiration approaches; it works against option buyers (time decay loss) and in favor of option sellers (time decay gain).[ CORRECT ]

[ D ]Theta is strictly positive for all option buyers across all strikes.

Takeaway

Theta measures how much an option's time value erodes per day as expiration approaches; it works against option buyers (a daily drag on their position) and works in favor of option sellers (a daily gain as the premium they collected decays).

Derivation

An option's premium is composed of intrinsic value plus time value, and time value shrinks continuously as fewer days remain for the underlying to make a favorable move — this decay accelerates as expiration nears, especially for at-the-money options. A long option holder (buyer) is fighting this daily erosion: even if the underlying price doesn't move at all, the option loses value purely from the passage of time, meaning theta is effectively 'negative' for the buyer's position.

Why the others fail

A — Theta measures the option's sensitivity to central bank interest rate changes.

Interest-rate sensitivity is measured by the Greek 'Rho', a separate sensitivity measure entirely distinct from Theta, which specifically isolates the effect of time decay on an option's premium.

B — Theta measures the exact default probability of the underlying company.

Default probability of the underlying company is a credit-risk concept relevant to corporate bonds, not an option Greek; Theta measures time decay of an option's premium.

D — Theta is strictly positive for all option buyers across all strikes.

Theta is negative, not positive, for a long option buyer's position under normal conditions — time decay works against the buyer, eroding value daily, rather than benefiting them.