# Theta

## Basic Points

- Theta is the measurement of how much an option's price changes relative to time.
- Often used to mean time decay, theta gets stronger in an accelerated fashion as the time of an option runs out.
- If long an option, then time decay causes net losses (unless more is earned for increases in implied volatility or sharp and favorable price movements).
- And if short an option, then time decay causes net profits (unless more is lost from increases in implied volatility or sharp and unfavorable price movements).

## Advanced: Dynamics

In the basic course of an option's time decay (aside from acceleration of it from decreasing IV and deceleration from increasing IV) it will decrease proportionate to the square root of time.

This time decay looks like a square root function with the x-axis reversed, as pictured in the second figure here to illustrate the acceleration of time decay as it approaches expiration.

<*Square root function retrieved from Wolfram Alpha and the inverted x-axis depiction is from Theotrade*>

With respect to the dynamics, the behavior of theta changes dramatically depending on moneyness (which is how far OTM or ITM the option is).

As Sheldon Natenberg explains in Options Volatility and Pricing, “Early in the option’s life, the rate of decay (the slope of the theoretical-value graph) is similar for each option. But late in the option’s life, as expiration approaches, the rate of decay slows for in-the-money and out-of-the-money options, whereas it accelerates for an at-the-money option, approaching infinity at the moment of expiration” (2015, p. 142).

Another important dynamic is that theta is proportionate to implied volatility and also the amount of time remaining. This means that for an ATM option, the theta at an IV of 40% is exactly double the theta at an IV or 20%, but that this relationship breaks down away from the money in either direction (p. 142).

Anyone experienced with writing options is familiar with the temporary pain of being on the other side of an IV spike, and seeing how that elevated IV increases the theta, which means that it would have been more profitable to open that same position at that later time.