For example, an option which is worth $4.83 today may only be worth $4.79 tomorrow and $4.55 next week, without the market moving.
This process is known as time decay.
Theta measures the speed of time decay – how much option premium will decrease in one day.
Example - Theta
Consider a $100 strike call option with 3 weeks (21 days) left to expiration.
Its underlying stock is trading at $101. The option’s premium, currently at $4.83, consists of intrinsic value (101 – 100 = $1) and time value (4.83 – 1 = $3.83).
The option’s theta is -0.04.
It means the option premium will decrease by 0.04 to $4.79 until the next day (as number of days to expiration decreases by 1), if everything else remains the same.
We could also say the option’s time value will decrease by 0.04 to $3.79, because passing time only affects time value; intrinsic value can change only if underlying stock moves.
Let’s assume nothing happens in the market until the next day. The stock stays at $101 and the option is indeed trading at $4.79.
Now it has 55 days left to expiration and theta of -0.04, indicating that the premium will decrease to $4.75 until the next day.
Theta Values
Options generally have negative theta – lose value with passing time.
There are some rare exceptions, but for now it is safe to take it as a universal rule.
Short option positions have positive theta and benefit from time decay (unless other factors like underlying price or volatility move against them).
In general, at the money options have greatest (most negative) theta, as they have more time value to decay than out of the money or in the money options.
Moneyness (the relationship between underlying price and strike price) is only one of several factors affecting theta.
Theta Units
Long time horizon may measure theta in weeks, while short term traders or those working with options very close to expiration may measure theta in hours or shorter intervals.
Calendar or Trading Days?
When using calendar days, theta means how much the option or portfolio value will change in one calendar day.
When using trading days, it is per one trading day.
We take 252 Trading Days as Saturday & Sunday .
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.
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.
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.
How Theta Changes with Passing Time
Theta of options which are near or at the money tends to increase (in absolute terms) with passing time.
When there are still several months left before expiration, the rate of time decay is relatively slow, and it accelerates as expiration approaches.
At the money options have greatest theta in the final days before expiration.
Options which are further out of the money or deeper in the money tend to lose most of their time value earlier.
How Theta Changes with Volatility?
The effect of volatility on theta is simple: Higher volatility means more time value and higher theta, other things being equal.
Theta Trading Considerations
The idea of making money “automatically” from passing time can tempt some inexperienced traders to treating positive theta strategies as sure ways to profits.
Understand that mere passage of time can never, on its own, generate returns higher than the risk-free interest rate.
Options on many underlying tend to trade at inflated prices, higher than what actual realized volatility would justify. This is called volatility risk premium.
The source of their profits is not passage of time itself; it is passage of time combined with mispriced volatility.
Theta and Gamma Relationship
Long option positions generally have negative theta and positive gamma (you pay for buying optionality).
Short option positions have positive theta and negative gamma (you get paid for providing optionality).
Positive theta is good: you make money with passing time. Negative theta is bad.
An ideal position would have positive gamma and positive theta. Unfortunately, there is no such option strategy.
Positive gamma is good: if the underlying price moves in your favor, your profits accelerate; if it moves against you, your losses slow down.
Negative gamma is bad: accelerating losses and decelerating profits.
Every strategy has strengths and weaknesses. It can position you favorably to either market moves or passage of time – but not both, as one pays for the other
Option theta and gamma provide quick information on where you are in this tradeoff.
Conclusion
Theta measures how much an option’s price will change in one day.
All options (with some rare exceptions) have negative theta – lose value with passing time.
Theta is greatest at the money. At the money theta is greatest just before expiration.
An increase in volatility increases time value and thereby theta.
Short option positions have positive theta and profit from passing time.
Positive theta goes hand in hand with negative gamma. There is no free lunch.
