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TL;DR

The rate of change of option price with respect to time: \( \Theta = \frac{\partial V}{\partial t} \). Typically negative for long options (time decay), reflecting the erosion of time value.

By Valenke Exam Prep Team·Last updated 2026-06-03

Theta (Greek)

The rate of change of option price with respect to time: \( \Theta = \frac{\partial V}{\partial t} \). Typically negative for long options (time decay), reflecting the erosion of time value.

Why it matters for interviews

Theta represents the cost of holding an option position. Understanding the theta-gamma tradeoff is essential for options trading: you pay theta to be long gamma, or collect theta to be short gamma.

Definition and Mathematical Foundation

The rate of change of option price with respect to time: \( \Theta = \frac{\partial V}{\partial t} \). Typically negative for long options (time decay), reflecting the erosion of time value.

Application in Quantitative Finance

Theta represents the cost of holding an option position. Understanding the theta-gamma tradeoff is essential for options trading: you pay theta to be long gamma, or collect theta to be short gamma.

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Frequently Asked Questions

Why does theta accelerate near expiration?▼
Time value is proportional to \( \sqrt{T} \). The derivative of \( \sqrt{T} \) is \( 1/(2\sqrt{T}) \), which increases as T approaches zero. ATM options experience the most dramatic theta acceleration.
Is theta always negative for long options?▼
Almost always. The exception is deep ITM European puts with high interest rates, where the present value benefit of delayed exercise can make theta slightly positive.
What is the Black-Scholes theta-gamma relationship?▼
From the Black-Scholes PDE: \( \Theta + rS\Delta + \frac{1}{2}\sigma^2 S^2 \Gamma = rV \). For a delta-hedged position: \( \Theta + \frac{1}{2}\sigma^2 S^2 \Gamma \approx 0 \). Theta and gamma are linked.