In general, to first order, option prices rise with the square root of duration (i.e., time-to-expiration).
I was just looking at puts on U.S. ETF FXI
and they grossly violate this rule. With FXI
trading at 39, the current ask on strike 35 puts (i.e., ~10% OTM) is as follows:
Days to Exp Ask Implied Vol Sqrt(Duration) $/Day
22 $0.07 29% 4.7 $0.015
50 $0.22 27% 7.1 $0.031
78 $0.35 25% 8.8 $0.040
113 $0.70 24% 10.6 $0.066
This makes no sense: Even though the implied vol on the longer duration options is lower, the price per day increases vastly faster than $\sqrt{Duration}$. (In fact, it is roughly $Duration^{1.5}$!) What am I missing?