## 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 an option's time decay. If everything is held constant, the option loses value as time moves closer to the maturity of the option. Theta is generally expressed as a negative number and can be thought of as the amount by which an option's value will decline every day.

Theta is drawn from the Greek alphabet and has numerous meanings across different fields. In the world of economics, theta can also refer to the reserve ratio of banks in economic models.

#### Theta

## Understanding Theta

Theta is part of the group of measures known as the Greeks, which are used in options pricing. The measure of theta quantifies the risk that time poses to option buyers, since options are only exercisable for a certain period of time.

### Key Takeaways

- Theta refers to the rate of decline in the value of an option over time.
- If all other variables are constant, and option will lose value as time draws closer to its maturity.
- Theta, usually expressed as a negative number, indicates how much the option's value will decline every day up to maturity.

Options give the buyer the right to buy or sell an underlying asset at the strike price before the option expires. If two options are similar, but one has a longer time until it expires, the longer-term option will have more value since there is a greater chance (given more time) that the option could move beyond the strike price.

## Differences Between Theta and Other Greeks

The Greeks measure the sensitivity of options prices 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. 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 extrinsic 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.

Put a different way, option values are composed of both extrinsic and intrinsic value (if applicable). At option expiration, all that remains is intrinsic value, if any, because time is a significant part of the extrinsic value.

### Key Takeaways

- Theta measures the daily rate of price decline in an option's value as it nears its expiration date.
- Option writers are the main beneficiaries of the decline in an option's value because it becomes cheaper for them to buy back the options to close out short positions.

## Theta Example

Assume an investor purchases a call option with a strike price of $1,150 for $5. The underlying stock is trading at $1,125. 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. This is unfavorable to the option holder. Assume the underlying stock remains at $1,125 and two days have passed. The option will be worth approximately $3. The only way the option becomes worth more than $5 again is if the price rises above $1,155. This would give the option at least $5 in intrinsic value ($1,150 - $1,150 strike price), offsetting the loss due to theta or time decay.