# Why theta multipled by days to expiry exceeds the total time premium of the option

Sometimes, I find an option where the total time value of the option may be 5 cents(rest is intrinsic value) and there are about 15 days to expiry and theta is .08 (8 cents).

How is this possible. If it is decaying 8 cents a day, then in 15 days, it will lose 120 cents of time premium( and that is assuming a linear time decay, which is not true), but time premium is only 5 cents to start with. So total time decay can only be 5 cents. So how can it keep decaying at 8 cents/day for 15 days?

Please look at AAPL 102 call with underlying ~130, and the call is asking 28.05. So time value of this call is ~ 28.05 - (130-102) = 0.05

Theta is 0.0882. There are ~ 15 days to expiry. Today is feb 27 ## 1 Answer

It is because theta is not premium / days to expiration. Theta is a "local" decay, measure of current rate of option decay, which is not assumed to stay constant.

In the example you provided, theta will be closer to zero (decay rate will slow down) as you approach expiration.

• Thanks. Bu the graph of theta decay shows that the decay accelerates closer to expiration. So why in this case, it will slow down? – Victor123 Mar 5 '15 at 14:28
• @Victor123 You are probably looking at option price chart, not at theta chart. Theta approaches zero as you get closer to expiration. – onlyvix.blogspot.com Mar 6 '15 at 14:27