Description of Option Theta

Options Theta arithmetic

You don’t need to understand the math behind theta (go on to the next section if you want), but for those interested, theta is more formally defined as the partial derivative of the option price with respect to time. will be

The call option formula is (this requires some knowledge of the normal distribution to understand):

Whether you are an option holder or a writer, you need to understand theta.

This Greek indicator will help you make the right decisions and ensure your investment success.

Because theta has different meanings in other fields (such as economics, which refers to bank reserve ratios), it is important to learn what theta means when it comes to options trading.

How is Theta different from other Greeks?

All other options Greece indicators measure how the price of an option is affected by a particular variable. For example, vega measures how sensitive the price is to a 1 percentage point change in implied volatility.

Option delta indicates how the price of the option is affected by every dollar change in the underlying asset, and option gamma indicates how a dollar change in the underlying asset affects the delta. increase.

finally, Low Measures sensitivity to changes in interest rates.

Unlike all of the above, Theta is not price sensitive. Instead, it measures time decay.

What is Theta?

Theta measures how the value of an option degrades over time. Simply put, it is the time decay of an option expressed in dollars or premium amounts. Although theta can be calculated in weeks, it is common to represent the decay of time by days.

All other factors held constant, options lose value as they approach their expiration date. Because of this, theta is usually negative. However, it should always be kept in mind that significant increases or decreases in the price of the underlying asset or changes in implied volatilities can also affect option prices.

To calculate how theta affects the option price, let’s imagine that the call option is currently at $3 and theta is -0.06. This means that the option price will fall by $0.06 per day. After one day, the option price drops to $2.94. After one week the price will be $2.58.

Effects of passage of time on theta

Theta of long term options is close to 0 and there is no loss of daily value. Short term options have the highest time value and have a higher theta because they lose more premium each day.

Theta is highest when the option is in money and lowest when it is out or in the money. Options near the money or near the money increase in theta value as the option nears expiration.

However, deep-in-the-money or out-of-the-money options experience a decline in theta value as the option nears expiration.

Moreover, the time decay is especially noticeable when the option is out of the money. Note that if the option is out of the money, the underlying asset will be below the strike price for calls and above the strike price for puts.

Therefore, as an out-of-the-money option nears expiration, it is less likely to become in-the-money.

theta curve

The key point is that the time decay is not a linear descent, even if all other factors remain equal. As the option expiry approaches, the theoretical time decay increases (meaning theta increases dramatically) because the option has less time to move. This leads to the so-called theta curve. The curve shows a slow decay in the early stages and an accelerated decay as the option nears maturity.

The pricing model accounts for weekends and trading holidays by adjusting for volatility or expiration. This means that the decay is seen over the 7 days, regardless of the actual number of trading days in the week. This also means that you can’t fool the system by opening a new short position late Friday and closing it early Monday so he gets two days of free time decay.

For the same reason, it is recommended to close positions on Fridays if a reasonable profit is being made. Waiting until Monday is unlikely to yield a larger profit. Additionally, if you change your mind, you can often re-enter the position on Monday at about the same price you exited at.

Nonetheless, there is no standardized way to represent optional time decay, so different time decays may appear depending on the model used.

Why is theta important?

Theta quantifies the risk faced by option buyers and writers over time. This risk exists in options trading because you only have the right to buy or sell the option’s underlying asset at the strike price before the expiration date.

Therefore, if two options have similar characteristics, but one expires further in the future, the longer option is worth more. This is because the option’s longer duration increases the likelihood that the option will exceed the strike price.

This all hinges on the fact that option values have an intrinsic value and an extrinsic value. Intrinsic value is the profit from an option based on the difference between the strike price and the market price.

External value refers to all that remains of the premium, the value of holding the option and the likelihood that the option will increase in value as the underlying stock price changes. All else being equal, the option’s external value declines over time, leaving only the internal value at expiration.

volatility and theta

generally, higher volatility Its underlying theta is higher than similar options on low volatility stocks. The reason is that options with high volatility have a higher time value premium. This means that your potential losses are higher each day.

To put this in context, let’s use another example. This time, assume the call option is currently at $5, the underlying stock is trading at $1,030, and the strike price is $1,045. Also, suppose the option has an expiration of 10 days and a theta of -0.5. This means that the option value decreases by $0.50 every day.

If everything remained the same, the option would have already lost $2.50 by the end of the 5th day. However, if volatility causes the price of the underlying stock to rise, it may offset losses for option holders calculated by Theta. In the example above, the price of the underlying asset must increase to at least $1,050 to make the option intrinsic value $5.

positive and negative theta

We said earlier that theta is generally negative, so it can also be positive. This is because both option buyers and option sellers can use theta.

If the position is net long, theta will be negative. Therefore, to be profitable as a buyer, he needs one of the two. You need to react quickly to get the direction right or have implied volatility on your side. In the latter case, we would like the implied volatility to grow more than theta can dampen the value of the option.

Negative theta is the reason why it is important to hedge long options with short options. For example, calendar spreads, vertical spreads, and diagonal spreads are preferable to long naked options. Doing so eliminates some (or all) of the time decay.

If the position is net short, theta will be positive. A positive theta is favorable because option writers want to lose the value of their position. Moreover, it is cheaper to buy back options to close short positions.

How to use theta

As already mentioned, all other factors being equal, theta decreases every day. This means you lose money every day when you buy options. When you choose to buy an option, you are hoping that the factors will not stay the same, i.e. the price of the underlying asset will fluctuate significantly.

Alternatively, Theta presents a good opportunity to short an option when the underlying asset price seems to change little. You make a profit because the option depreciates over time.

Of all the Greek languages, Theta is the most indefinite. Theta is often inaccurate because the calculation must assume that implied volatility and price movements are stable (which, of course, may not be the case).

For this reason, theta should never be considered in isolation, but as part of the bigger picture.

List of positive theta option strategies

List of negative theta option strategies

*About the Author: Chris Young has a degree in Mathematics and 18 years of experience in finance. Chris is British, but he has worked in the US and most recently in Australia. His interest in options was first sparked by the “Trading Options” section of the Financial Times of London. He was determined to pass this knowledge on to a wider audience and in 2012 founded Epsilon He Option.*

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