I understand Theta is time decay and this decay speeds up when we are near expiration. Apart from that, I don’t understand. If we have a 30-day and 60-day long call, will theta be higher in 30 days than 60 days?
Also if I am short a call and I have one short call with 6 months expiration and another with 2 months expiration where is theta higher?
Anyone please?
One way to understand it is to go back to what drives the value of the option.
Imagine possible paths of the stock over a period of time, 10 days say. So over those 10 days, on any given day, the path of the stock follows some random walk. After 10 days, the stock has some probability of being between -S and +S.
Now add one more day. So between day 10 and day 11, if the stock was near S, on day 11 it has some probability of moving even higher to S’>S. The stock price is modelled as a diffusion process with drift.
So this means the range of values the stock could be in with some probability after 11 days is bigger than after 10 days.
Thats what drives the theta (plus the time value effect on the expected gain, but that’s technical).
The longer the expiry, the greater the range of outcomes, the greater the value of the option the more theta you pay for when you buy an option.
So day after day, the value of the option reduces through by theta because the range of outcomes reduces.
Thanks for the reply. So if understand this correctly, a 60-day option has a higher range of outcomes, so the theta here would be more than a 30-day option. But in short (call/put), a 30-day would have a higher theta than a 60-day because a 30-day has a lesser range of outcomes which works in favor of the seller
Did I understand this correctly?
Roughly speaking yes, but its not so simple.
It also depends how far out of the money the option is. If an option is heavily OTM, then there are very few outcomes for it to expire profitably. Then one more day doesnt do that much for dispersion of outcomes. So then theta is dominated by the time value of money effect, so rates.
So a 30 day option could possibly have a higher theta than a 60 day option, if it is sufficiently more in the money and rates are well behaved.
Gotcha! Thank you!