## What Is Theta?

The term theta refers to 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 of an option. This means an option loses value as time moves closer to its maturity, as long as everything is held constant. Theta is generally expressed as a negative number and can be thought of as the amount by which an option's value declines every day.

### Key Takeaways

• Theta refers to the rate of decline in the value of an option over time.
• If all other variables are constant, an 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.

## Understanding Theta

Theta is part of the group of measures known as the Greeks, which are used in options pricing. Remember—options give the buyer the right to buy or sell an underlying asset at the strike price before the option expires. The strike price, which is also called an exercise price, is set when the contract is first written, informing the investor of the price at which the underlying asset must reach before the option can be exercised.

The measure of theta quantifies the risk that time poses to option buyers since options are only exercisable for a certain period of time. This is known as time decay or the erosion of the value of an option as time passes. An option's profitability decreases as time goes on. But what happens when two options are similar but one expires over a longer period of time? The value of the longer-term option is higher since there is a greater chance or more time that the option could move beyond the strike price.

Because theta represents the risk of time and the loss of value of an option, it is always expressed as a negative figure. The value of the option diminishes as time passes until the expiration date. Since theta is always negative for long options, there will always be a zero time value when the option expires. This is why theta is a good thing for sellers but not for buyers—value decreases from the buyer's side as time goes by, but increases for the seller. That's why selling an option is also known as a positive theta trade—as theta accelerates, the seller's earnings on their options increase.

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## Special Considerations

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 works against long option holders.

Conversely, time decay is favorable to an investor who writes options. Option writers benefit from time decay because the options 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, if applicable, composed of both extrinsic and intrinsic value. At option expiration, all that remains is intrinsic value, if any, because time is a significant part of the extrinsic value.

## Theta vs. Other Greeks

The Greeks measure the sensitivity of options prices to their respective variables. For instance, the delta of an option indicates the sensitivity of an option's price in relation to a \$1 change in the underlying security while 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.

Drawn from the Greek alphabet, theta has numerous meanings across different fields—in economics, it also refers to the reserve ratio of banks in economic models.

## Example of Theta

Let's 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 (\$1,155 - \$1,150 strike price), offsetting the loss due to theta or time decay.