*The Business Professor*, updated February 22, 2020, last accessed September 26, 2020, https://thebusinessprofessor.com/lesson/theta-definition/.

### Theta Definition

Theta evaluates the value of the options price to the passing of time. This calculates the rate, at which the price of options is particularly in terms of time value, rises or decreases as the time to expire approaches. For example, if an option is worth $1.50 and it has a theta of 0.05, this means that in the next 24 hours the option will drop 5 cents in value, all things being equal. So if nothing else happens (the spot commodity doesn’t change in price, the implied volatility remains the same and so on), if we look at the theoretical value of our option tomorrow, the pricing model will say $1.45.

### A Little More on What is Theta

With the price change or the underlying stock fluctuations, you need to understand how it would affect your options pricing. Greeks in options help us understand how the different factors like prices, expiry time, and volatility affect options pricing. Theta as a sub-measure under Greek informs us how much the value of our option will change over time.

A contract options comprises at least four components: size, expiry date, strike price and premium. The expiry date is the date after which the option is no longer exercisable by a trader. The strike price is the price at which the asset will be purchased or sold (in the event that the option is exercised by the contract buyer).

### Differences Between Theta and Other Greeks

The Options’ Greeks are methods designed to measure some of the multiple factors influencing a contract’s price. In particular, they are statistical values are used to calculate the probability of a given contract based on different fundamental variables. Delta analyses how much the price of an options contract will change with respect to the price of the underlying asset. Gamma tests the rate of change over time in Delta. Vega calculates the rate of change in a contract price compared to a 1 percent change in the underlying asset’s implied volatility. An increase in Vega would normally reflect a rise in both calls and puts prices.

### Theta for Option Buyers vs. Option Writers

Option buyers should be well aware that theta steals time value at the highest rate in the last month before expiry of option. Every time you purchase an option, the value of that option is tied to volatility and so to make money it either depends on moving closer to the money or to increased volatility. Theta decay is also inherent in long options and will always lose value over time on that front. On the other hand, option sellers do really like theta. Theta offers scant advantage when selling options that are longer-dated. Option sellers tend to sell close to expiration date for profitability.

- Greeks help us understand how the various factors such as costs, expiry time and uncertainty impact options pricing.
- The strike price is the anchor price at which both the option buyer and the option writer concluded an agreement.
- The underlying price is merely the Asset’s spot price.
- Time moves in one direction and thus Theta is a positive number.
- Everything else equal, due to Theta, options lose money every day.
- Theta is a valuable Greek to option sellers.
- Volatility is a risk-indicator.
- Option sellers always have the time-risk compensated.
- Implementation of an option contract is the act of claiming your right to buy the options contract at the expiry time.

### Theta Example

Theta or factor in time decay is the rate at which an option loses value as time goes by. For example, if an option writer has sold options at $54, with theta at 0.75, all the other options being equivalent, the same option is likely to trade at

– = 0.75 * 3 = 2.25 = 54 – 2.25 = 51.75

The seller can therefore opt to close the option position on T+ 3 day by buying it back at $51.75/- and making a profit of $2.25. Considering that options lose value on a regular basis, the seller of the option will benefit from keeping the premium to the degree that it loses value due to time.

References for “**Theta****”**

https://en.wikipedia.org/wiki/Theta

https://www.quora.com/What-is-Theta

https://www.investopedia.com › Investing › Options