I wonder if the takeaway strategy for me is to stuff my money in my mattress. If they are truly undervalued, then buying/not selling makes sense. The thing is, I don't believe that the distro of option prices actually implies a lognormal distro. If they did, there probably wouldn't be a skew (I think). So the reality is that people use the BSM model, but "tweak it" (again, I think).
If it is pure brownian, it doesn't matter, but in fact it is not. My gut feeling is that the fat tail effect on a daily basis is larger than the monthly. The reasoning is simply the law of large number. Thats why when we apply probability (or statistics) in option trading, it is better to look at longer term, instead of day-trading options. I don't know if anyone has any backtesting software to test option strategies. If anyone has one, I like to look at the statistical result of a simple strategy "buying a 1 sigma call every month".
My recollection is probably worse than yours but I seem to recall that the notions of "variance", "mean", "skew" and "kurtosis" are not really defined under Cauchy distributions. These distributions are instead characterized and located with a location & scale parameter. Given this observation I fell back on simple high school definitions of kurtosis which generally imply that sharper peaked distributions imply fatter tails than less peaked distributions. My mistake is probably in assuming that Cauchy distributions are less peaked than leptokurtotic distributions. But in fact "higher kurtosis" is not really defined under Cauchy since it has no 4th order moment around the undefined concept of a "mean". So I may have made the mistake of assuming leptokurtotic distributions are generally much more "peaked" than Cauchy but they really are two completely different animals - and Cauchy is a strange one at that. I guess I really don't know how to characterize "fat tails" in the context of Cauchy since there are some notional difficulties in the entire concept of "shape" that may not permit a direct comparison between the two distributions nor infer relative differences in tails. I appreciate your tremendous insight. TS
I think, you are on to something here yip. I think there is a "windowing effect" in the options calendar period itself that is clipping and forcing a rationalization of the market as calendar ticks toward expiration. Now - how to profit by this or avoid losses if true?. At least with SPX as a European style option we can't be assigned on any short positions on a daily fat tail event. So if one is confident in their position would the implication be to hang tough through expiration if a position started going against us and maybe even opportunistically go long if premium was discounted at the time a short position was threatened? I am beginning to favor the "stuff it in the mattress" strategy that somone mentioned. TS
TS, I believe most successful traders don't realize that they are successful because they have a "statistical" edge, and they thought it is a "perceived" edge. For example, a "successful" naked writer consistently makes money for over 20 years. Why? Because they sell the "overvalued" options and buy back when it is "undervalued". Let me explain. If ugly's distribution is true, the atm options are undervalued, and CTM options are overvalued (compared to atm). If I sell CTM options, and my rule is to cover it when it is ATM. It means, I sell overvalued options and buy undervalued options. Statistically it gives them an edge that they didn't realize. Of course, I didn't mention the risk management part and the position sizing, that are the most important part in long-term trading success. I wish it explains why some of us have found "successful" and "consistent" naked writers.
That is quite a theory yip1997, but the naked premium writer phenomena is easily explained by randomness. Take a large universe of naked premium writers and then remove the population with negative returns. The strategy will appear superb based on the returns of the remaining population. -segv
Being 'confident' does make the market go your way. 'Hanging tough' is a shortcut to bankruptcy. That's my 2 cents, based on more than 30 years experience as an option trader. Mark