What is Theta in Options Trading and How Does it Work?

Theta is the Greek that measures the rate of decay of an option's extrinsic value relative to the passage of time. Extrinsic value is time and volatility value, where intrinsic value is value that does not decay and is static based on where the stock price is relative to the strike price. This decay concept is often referred to as "time decay," because all else being equal, options lose extrinsic value as they get closer to expiration. 

Theta is typically expressed as a negative number and indicates how much the option's extrinsic value will decrease every day, all else being equal. This is because as time passes, the option has less time to move into a profitable position, and so its extrinsic value decreases.

For example, if an option has a theta of -0.05, the option's price would decrease by 5 cents per day, assuming all other variables remain constant. This decrease accelerates as the option approaches its expiration date.

Theta measures the rate at which an option's price is expected to decay for each day that passes, assuming that all other factors remain the same. This rate of decay tends to accelerate as the option approaches its expiration date, a phenomenon often referred to as "time decay."

Here's how theta works for options buyers versus options sellers:

• Options Buyers: If you're the holder (buyer) of an option, theta can work against you. Each day that passes reduces the amount of time for the option to become profitable (or more profitable if it's already in-the-money). For instance, if you own a call option with a theta of -0.05, the extrinsic value of your call option will drop by 5 cents per day, all other things being equal.

• Options Sellers: If you're the writer (seller) of an option, theta can work in your favor. The premium you received when you sold the option gradually decays as time passes. That’s because with each passing day, there's theoretically less time for the underlying asset to move in a way that would make the option profitable for the buyer. If the option is out-of-the-money at expiration, it will expire worthless, and as the seller, you get to keep the entire premium received up front on trade entry.

It's important to note that theta is just one factor influencing the price of a given option. Other factors include the price of the underlying asset, the strike price of the option, the risk-free interest rate, and implied volatility (i.e. vega). 

Also, it’s important to keep in mind that like the other Greeks, theta is dynamic, and can change over time. Theta generally gets larger (in absolute value) as an option gets closer to expiration.

Theta measures the rate of decline in the value of an option due to the passage of time. It's typically expressed as a negative number and indicates how much the option's value will decrease every day, all else being equal. This is because as time passes, the option has less time to move into a profitable position for the buyer, and so its extrinsic value decreases.

For example, if an option has a theta of -0.05, the option's price would decrease by 5 cents per day, assuming all other variables remain constant. Theta generally gets larger (in absolute value) as an option gets closer to expiration.

Theta is calculated using complex mathematical models like the Black-Scholes model, Bjerksund-Stensland model, or the Binomial options pricing model.

These models incorporate several variables to derive the option's theta, including the current stock price, the option's strike price, time until expiration, risk-free interest rate, and the volatility of the underlying asset.

In practice, it's not common for individual traders to calculate theta themselves due to the complexity of the models required. Instead, traders usually rely on the theta provided by their trading platform or other financial software, and ensure they have an understanding of how theta may work for or against their options position.

Looking at an example, imagine you buy a call option for $2.00 with a strike price of $50 that expires in 30 days. The underlying stock is currently trading at $48.

Now, let's say this option has a theta of -0.05. This means - all else being equal - the price of your option will decrease by $0.05 each day due to time decay.

So, after one day, if all the other factors remain unchanged, your option might be worth $1.95 (down from the initial $2.00). And after two days, it would theoretically be worth $1.90. 

However, theta decay can accelerate as the option gets closer to expiration, which is something to keep in mind.

As an options buyer, theta is theoretically working against you, eroding the value of your option with each day that passes. But if you were the one who sold (i.e. wrote) the option, theta would theoretically be working in your favor, making the option cheaper to buy back if you wanted to close your position.

Remember, theta is just one piece of the puzzle in options pricing. Other factors can impact the value of a given option, such as the price of the underlying stock, volatility (i.e. vega), and the risk-free interest rate. Moreover, the actual market can often behave differently than the theoretical model, so actual results can vary.

Theta is presented as a negative number for option owners, meaning that the extrinsic value of the option decreases as time passes, all else being equal. This is referred to as time decay. However, theta is positive for short options, indicating that time decay is theoretically beneficial for the option seller.

When we say an options position has "positive theta," that means the short options position is set up to potentially benefit from the passage of time. In other words, the total value of the position increases as time goes by, assuming all other factors remain constant. 

That’s because the option that has been sold will decrease in extrinsic value over time due to time decay, which theoretically benefits the option seller.

However, it's important to keep in mind that while time decay is beneficial for options writers, selling options can still be risky. For instance, if the price of the underlying security moves significantly against the position, the potential losses for an option writer can be substantial.

Moreover, a position with “positive theta” isn’t guaranteed to turn a profit, just as a position with “negative theta” isn’t guaranteed to turn a profit. 

Theta is negative for long options, meaning that the value of the option decreases as time passes, all else being equal. This is referred to as time decay. 

So, when you see that an options position has "negative theta," it means that the position will lose value as time passes, all else being equal.

This is a crucial consideration for options buyers, as they need the price of the underlying asset to move in the desired direction rapidly enough to offset the loss of value due to time decay.

It’s important to note that a position with “negative theta” isn’t guaranteed to turn a profit, just as a position with “positive theta” isn’t guaranteed to turn a profit. 

"Moneyness" in options trading refers to the relationship between the current price of the underlying asset and the strike price of the option. It gives traders an idea of the intrinsic value of the option.

There are three states of moneyness:

• In-the-Money (ITM): This means the option has intrinsic value that does not decay if it remains ITM through expiration

• At-the-Money (ATM): This means the underlying asset's current price is equal (or nearly equal) to the option's strike price. The option may not have intrinsic value now, but it may still have extrinsic value due to the time remaining until expiration and implied volatility (i.e. extrinsic value). If the option moves ITM, it then has intrinsic value that does not decay.

• Out-of-the-Money (OTM): This means the option does not have intrinsic value and would completely decay if it remains OTM through expiration. The option doesn’t have intrinsic value now, but it may still have extrinsic value due to the time remaining until expiration and implied volatility . If the option moves ITM, it then has intrinsic value that does not decay.

At-the-money options tend to have the highest theta. That’s because these options often have the highest extrinsic value (also known as time value), which is most susceptible to time decay. Therefore, at-the-money options tend to lose value at a quicker rate than in-the-money or out-of-the-money options, as they approach expiration.

On the other hand, in-the-money and out-of-the-money options theoretically have lower theta values. Deep in-the-money options have a high intrinsic value and low extrinsic value, while deep out-of-the-money options have no intrinsic value and low extrinsic value, so the amount of value they can lose to time decay is limited.

• Theta measures the rate of decline in the value of an option due to the passage of time. It's typically expressed as a negative number and indicates how much the option's extrinsic value will decrease every day, all else being equal
• For example, if an option has a theta of -0.05, the option's price would decrease by 5 cents per day, assuming all other variables remain constant. Theta generally gets larger (in absolute value) as an option gets closer to expiration
• The impact of theta is very different for buyers of options as compared to sellers (aka “writers”) of options
• Option sellers can benefit from theta, or time decay, because as each day passes, all else being equal, the value of an option decreases, which is advantageous for the option writer
• However, it's important to keep in mind that while time decay is beneficial for options writers, selling options can still be risky. For instance, if the price of the underlying security moves significantly against the position, the potential losses for an option writer can be substantial
• For option buyers, theta can represent a challenge, because the value of the option theoretically decreases as time passes, all else being equal. This is referred to as time decay
• A position with “positive theta” isn’t guaranteed to turn a profit, just as a position with “negative theta” isn’t guaranteed to turn a profit