  # Time decay in options: Observing the Effect of Theta

Movement of time

Time moves in one direction and so do the expiry days; as they pass, traders are not ready to pay as much towards time value. For example, I recently observed that with merely 5 days to expiration, they were willing to pay far less than if there had been 18 days left.

• Date = 29th April
• Expiry Date = 30th April
• Time to expiry = 1 day
• Strike = 190
• Spot = 179.6
• The intrinsic value is determined by subtracting the strike price from the underlying value. In this case, the calculation would be: 179.6 – 190 = -10, which results in a negative value.
• Therefore, the intrinsic value is considered to be zero.

Consequently, the remaining value of 30 paisa is attributed to the time value, which is equal to the premium. As the expiration date approaches with only 1 day remaining, traders are only willing to pay a minimal time value of 30 paise.

However, a 20-day expiry could command a time value of Rs.5 or higher. As the expiry date approaches, option buyers will pay significantly less for time value; for instance, if today they have paid Rs.10/-, tomorrow it could be lowered to Rs.9.5/-. This proves that options depreciate in their premium due to the passing of time alone and this is where Theta – the third Option Greek – makes its contribution by calculating the rate at which it happens.

– Theta

As the expiration date gets closer, both Call and Put options experience a decrease in value. Theta, which represents the rate of value decay over time, is expressed as the number of points lost per day when all other factors remain constant. Although theta is always positive, it is commonly denoted as a negative figure to highlight the diminishing value. For example, if an option is currently priced at Rs.2.75/- with a theta of -0.05, it is expected to trade at Rs.2.70/- on the next day, assuming all other factors remain unchanged.

Long options buyers have a notoriously negative theta which means they stand to lose more than they’d gain over time if nothing else changes in their favour. In contrast, short options sellers profit from the positive theta since their objective is to retain premium and therefore capitalise on money lost through time decay alone as long as everything else does not move against them drastically – for example if an option writer has sold options at Rs.54 with a theta of 0.75, and all else remains equal, then this option should trade at -(0.75 * 3) = 51.75 on T+3 day  allowing them to buy back at that price

1. At the beginning of the series, when there is a long time remaining until expiration, the option does not depreciate rapidly. For instance, when it had 120 days left it was priced at 350, declining to 300 with 100 days still to go. Therefore, the effect of time decay or Theta in this case is minor.
2. As we near the end of the series, the effect of theta is pronounced. We can observe that when there were 20 days until expiration, the option was valued at around 150, but by the time expiry is imminent, the decline in premium accelerates drastically (the option value drops below 50).

Selling options at the start of the series offers a great advantage in the form of a large premium value, as there is still a large amount of time value. Nevertheless, it is worth noting that the rate at which the premium decreases is relatively low.

Closer to expiry, while you get a lower premium, this rate is faster and more beneficial to you as an options seller. Theta is fairly simple to comprehend, and we will circle back to it when discussing cross dependencies of Greeks further down the line. So if you have been following thus far, we are now ready for understanding Vega – our final Greek!