Regarding the above said BSM sim discrepancy: I had used IV=11 but the market seems to have used IV=14.134 : Code: BSM simulations: 1) using IV=11 S=4221.0200 K=4280.00 IV=11.0000 S_Chg=67.9584 S_ChgPct=1.6100 (Sx=4288.9784) Calls: DTE=0.00 : C=8.9784 Prev=0.0646 Chg=8.9138 ChgPct=13800.93 DTE=1.00 : C=14.9753 Prev=0.6265 Chg=14.3488 ChgPct=2290.16 DTE=2.00 : C=18.8653 Prev=1.5838 Chg=17.2816 ChgPct=1091.15 DTE=3.00 : C=21.9098 Prev=2.7177 Chg=19.1921 ChgPct=706.18 DTE=4.00 : C=24.4968 Prev=3.9227 Chg=20.5742 ChgPct=524.49 DTE=5.00 : C=26.7859 Prev=5.1493 Chg=21.6366 ChgPct=420.18 DTE=6.00 : C=28.8609 Prev=6.3736 Chg=22.4874 ChgPct=352.82 DTE=7.00 : C=30.7727 Prev=7.5835 Chg=23.1892 ChgPct=305.78 DTE=8.00 : C=32.5546 Prev=8.7732 Chg=23.7815 ChgPct=271.07 DTE=9.00 : C=34.2299 Prev=9.9397 Chg=24.2903 ChgPct=244.38 DTE=10.00 : C=35.8158 Prev=11.0821 Chg=24.7337 ChgPct=223.19 DTE=11.00 : C=37.3252 Prev=12.2003 Chg=25.1249 ChgPct=205.94 DTE=12.00 : C=38.7681 Prev=13.2947 Chg=25.4734 ChgPct=191.60 DTE=13.00 : C=40.1527 Prev=14.3662 Chg=25.7866 ChgPct=179.50 DTE=14.00 : C=41.4856 Prev=15.4154 Chg=26.0702 ChgPct=169.12 2) using IV=14.134 S=4221.0200 K=4280.00 IV=14.1340 S_Chg=67.9584 S_ChgPct=1.6100 (Sx=4288.9784) Calls: DTE=0.00 : C=8.9784 Prev=0.3702 Chg=8.6082 ChgPct=2325.24 DTE=1.00 : C=17.6384 Prev=1.9140 Chg=15.7243 ChgPct=821.52 DTE=2.00 : C=22.7297 Prev=3.8653 Chg=18.8645 ChgPct=488.05 DTE=3.00 : C=26.6835 Prev=5.8900 Chg=20.7936 ChgPct=353.03 DTE=4.00 : C=30.0327 Prev=7.8889 Chg=22.1438 ChgPct=280.70 DTE=5.00 : C=32.9911 Prev=9.8310 Chg=23.1601 ChgPct=235.58 DTE=6.00 : C=35.6701 Prev=11.7078 Chg=23.9622 ChgPct=204.67 DTE=7.00 : C=38.1364 Prev=13.5194 Chg=24.6170 ChgPct=182.09 DTE=8.00 : C=40.4340 Prev=15.2687 Chg=25.1653 ChgPct=164.82 DTE=9.00 : C=42.5932 Prev=16.9598 Chg=25.6334 ChgPct=151.14 DTE=10.00 : C=44.6364 Prev=18.5970 Chg=26.0395 ChgPct=140.02 DTE=11.00 : C=46.5806 Prev=20.1843 Chg=26.3963 ChgPct=130.78 DTE=12.00 : C=48.4388 Prev=21.7255 Chg=26.7134 ChgPct=122.96 DTE=13.00 : C=50.2216 Prev=23.2240 Chg=26.9976 ChgPct=116.25 DTE=14.00 : C=51.9374 Prev=24.6830 Chg=27.2544 ChgPct=110.42
Ok, in simple terms: the percent payout is higher because their probability to end up in the money was much lower. Do you get the same lottery odds when someone offered you a game to flip a fair coin?
But IMO we agreed that predicting t is easier than predicting t+x. So, then IMO your above statement contradicts this fact... Computer: Please reformulate the question
There is no contradiction. An option with smaller odds to end up in the money trades relatively at a lower premium. A large move in the underlying then results in a larger percent change of premium, especially options with hardly any time value left. You may want to review some options basics.
New insights regarding the above analysis of the said last Friday where SPX had moved upto 1.61% or so wrt to previous day's close: AsOf=2023-06-02-Fr-151524-EDT DTE=0.00 US=4288.9000 Chg=67.8800 ChgPct=1.6100 ChgPctMon=62.55 ATM_IV_Avg=9.61 Delta_z=3.12206 ... ChgPctMon just means forward-transforming the 1.61% to monthly (it's not the real monthly change). A kind of "normalization" to make the ChgPct of different tickers comparable, but the Delta_z below is maybe better suited for this task. ATM_IV_Avg is the avg ATM IV of both Calls and Puts of all ExpireDates of the inspected next 14 days (cf. DTE list in above link). Delta_z is for the spot change in units of z (ie. that many StdDev's) wrt the previous close on the day before, ie. last Thursday. I don't have the HV for the SPX, so I instead used the above said ATM_IV_Avg to get the Delta_z. It means: that said past Friday was a "bigger than 3 sigma event" for SPX ! .
Quickly read your opening post follow regarding predictability of T vs T +X. You followed it up with profitability of short dated long options vs long dated.. 2 separate issues that really aren't related..
BTW, which other tickers with 0DTE options do exist currently? I know of the above said SPX, plus NDX, SPY, QQQ, RUT. Any others? The following is of course true: