Depending on how you look at it. Theta is not a pure exponential function of time. Theta has a factor which is an exponential function. Look at the theta formula. Also the bid ask quote is not continuous, so it won't follow a continous function. For example, 5 days before expiration, a FOTM option is quoted 0.05 and 0.1. This bid ask quote will not change for 2 or 3 days, and the last day it changes to 0 and 0.05. Only when the quote is large enough, we can approximate the discrete quotation by a continous function. In practice, it is fair enough to say it is exponential time decay if we allows a certain margin of error. Traders are not mathematicians. You cannot use pure math perspective to look at trading.
I never said that real theta is linear. I said that with the theoretical example, where the option price declined by exactly 5 cents a day due to theta (which would NEVER happen in reality, even if the stock didn't move at all), then in that case it would be linear.
You're not getting it. Let it go. "Five cents a day" would require an increase in vol to account for the gain in synthetic time.
There exists a relationship between volatility and time and it is as follows. An increase in iv has the same effect as an increase in time to expiry - thus 'synthetic time'. The reverse obviously also holds true, i.e if there is more time to expiry then that has the same effect as an increase in iv, iow premium goes up. db
This is not correct. Simply refer to a B-S model and take a careful look at the relation between option value and time variable.
Daddy I take your point, but I wouldn't say an increase in IV "has the same effect as increasing time". Adjusting one or both parameters to arrive at an option price maybe do-able, but there will be significant differences in the greeks, especially Theta.