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nism-series-xb-black-scholes-option-greeks-delta-gamma-theta[ INVESTMENT ADVISER (LEVEL 2) ]

In option risk management, what does 'Theta' (θ) measure in an option portfolio?

[ A ]The rate of change in option price relative to stock price (Delta).
[ B ]The rate of change in Delta relative to stock price (Gamma).
[ C ]The sensitivity of option price to changes in implied volatility (Vega).
[ D ]The rate of change in an option's price relative to the passage of time (Time Decay), measuring the daily loss in option premium as expiration approaches.[ CORRECT ]
Takeaway

Option D is correct: The rate of change in an option's price relative to the passage of time (Time Decay), measuring the daily loss in option premium as expiration approaches.

Derivation
The Greeks each isolate one distinct source of an option's price sensitivity, and Theta is the one tied purely to the calendar rather than to the underlying's price or volatility. As an option approaches expiry, the time value component of its premium erodes — usually expressed as a negative number representing the rupees an option loses per day, all else held constant. Theta accelerates as expiration nears, particularly for at-the-money options, so option buyers are effectively racing against a shrinking premium even if the underlying stays flat, while sellers benefit from that same erosion. This is distinct from Delta (price sensitivity), Gamma (rate of change of Delta), and Vega (sensitivity to implied volatility).
Why the others fail
A — The rate of change in option price relative to stock price (Delta).
Price sensitivity to movement in the underlying asset's price is what Delta measures, not Theta, which isolates the effect of time passing alone.
B — The rate of change in Delta relative to stock price (Gamma).
The rate at which Delta itself changes as the underlying moves is what Gamma measures, not Theta, which is unrelated to the underlying's price movement.
C — The sensitivity of option price to changes in implied volatility (Vega).
Sensitivity to shifts in implied volatility is what Vega measures, not Theta, which specifically isolates the erosion of premium purely from time passing.