Hey neww, yes, the higher the Implied Move the less likely you are to earn on your straddle. What I mean by tail risk (and I guess I should have not used it) is that you if buy a straddle with an implied move of 20% and the stock doesn't move. You just lost your whole (expensive) investment. If the stock is implying a 20% move, an actual move of say 2% is expected to be extremely low (tail risk on a long straddle). But your right, that's bad wording. *Edit, in my previous post I made a mistake. I meant to say, I have come the conclusion that buying a straddle..
I'm pretty sure that was a typo and that he meant to write the opposite. Late night, lots of coding... a sign error comes easily. Interesting plot. The densities show clear mixture structure. With n = 1400, probably not a statistical artifact. Likely an omitted moderator(s), With mixture structure that clear you have a very good chance of being able to identify that moderator(s). Fitting mixture distros is usually done via EM, which in this application is very prone to finding local minima. So either run it in a loop with various starting guesses and choose the one that matches your intuition from visual inspection of the original mixture density, or give it visually obvious starting values.
Here is an Rpub where they go over the EM in R and they run a loop as well. https://rpubs.com/H_Zhu/246450 However, I don't understand what you mean by various starting guesses. Also, to find the moderator I have to run a regression right? Y = i + aX + bM + cXM + E where I solve for M. But what happens once I solve for M? How do I interpret this lurking variable?
EM is an iterative algo so is typically itself run in a loop. I haven't looked at the link but that is probably what their loop involves. For fitting Gaussian Mixtures, you'll usually specify the number of mixtures; if not, the argument will loop over various mixture numbers and choose based on some information criterion, just like you can have the vars package guess the best number of lags for your VAR model using AIC. For fitting Gaussian Mixture distros, EM is usually implemented as a form of gradient ascent search in parameter space. The parameters are the location and scale parameters.of your n mixture densities. EM will start the search from (depending on the implementaion) either from random values for the n * 2 parameters, or by using random values between hueristically chosen uper and lower bounds. It is very prone to landing on local maxima, so if you run it three times, you'll get three different answers. You can usually guess good starting values from visual inspection of the mixture density plot. In your case, your mixture densities look like a mix of three or four sub-densoties the parameters of which (esp. the location parameters) you should be able to guess pretty well. The attached paper explains further. Don't get bogged down in the math of it -- just read the abstract and skim the introduction and conclusion sections. BTW, I posted the Toda Yamamoto paper because the algo was entirely in the abstract, I didn't mean for you to get into the somewhat obtuse mathematical exposition. If you want a clearer explanation of the "excess lags" method, there's a more recent paper that explains it well. I'll post it when I remember who wrote it. Ditto the original Box-Tiao method, the original paper is easier to get through than the Bewley version. Finding an omitted moderator is quite complex and starts with visual inspection of various plots. It is more art than science. I don't know of one "single source" reference on the subject. I'll pm you on it when I have the time.