# Theta

## What is 'Theta'

Theta is a measure of the rate of decline in the value of an option due to the passage of time. It can also be referred to as the time decay on the value of an option. If everything is held constant, the option loses value as time moves closer to the maturity of the option.

## BREAKING DOWN 'Theta'

Theta is the eighth letter in the Greek alphabet. It is part of the group of measures known as the Greeks, other measures include delta, gamma and vega, which are used in options pricing. The measure of theta quantifies the risk that time imposes on options as options are only exercisable for a certain period of time. Time has importance for option traders on a conceptual level more than a practical one, so theta is not often used by traders in formulating the value of an option.

## Differences Between Theta and Other Greeks

The Greeks measures the sensitivity of options prices in relation to their respective variables. The delta of an option indicates the sensitivity of an option's price in relation to a \$1 change in the underlying security. The gamma of an option indicates the sensitivity of an option's delta in relation to a \$1 change in the underlying security. The vega indicates how an option's price theoretically changes for each one percentage point move in implied volatility.

## Theta for Option Buyers vs. Option Writers

If all else remains equal, the time decay causes an option to lose its value as it approaches its expiration date. Therefore, theta is one of the main Greeks that option buyers should worry about since time is working against long option holders. Conversely, time decay is favorable to an investor who writes options. Option writers benefit from time decay because the options that were written become less valuable as the time to expiration approaches. Consequently, it is cheaper for option writers to buy back the options to close out the short position.

## Theta Example

For example, assume an investor purchases a call option with a strike price of \$1,150 when the underlying stock is trading at \$1,125 for a price of \$5. The option has five days until expiration, and theta is \$1. In theory, the value of the option drops \$1 per day until it reaches the expiration date. Therefore, the option loses approximately 20% of its value if all else remains equal. This is unfavorable to the option holder. Assume the option remains at \$1,125 and two days have passed. Therefore, the option is worth \$3.