Look at local-vol say strikes 0.5% off of ATM. You have 50bp differential. Contamination/stickiness expressed as skew flips with moves that are well inside 1SD on an hourly basis.
Since options are based on a probability distribution... which runs 0-100% and affects gamma, vega and delta directly... it can't be bi-modal. Since a bi-modal distr would mean it has two tops... which in turn means it would put a higher value/probability on on OTM to become ITM than the ATM... which is silly... since for an OTM to become ITM, the ATM becomse ITM first. Linearity between the strikes makes this impossible. Also... a bi-modal dist would mean the (extrinsic) premium of an OTM put (say 90 strike) and that of the OTM call (110 strike) would be bigger than the ATM strike put or call.... again... not going to happen. If it would... that's a serious arbitrage. I guess it could happen over different maturities... when you're looking at two different probability curves/distributions say 1 month and 6 month... the skew of both expiries can be totally different which might end up looking like some kind off bi-modal distribution mix... but you'd be comparing apples and pears.
Bi-modal implied risk-neutral densities are reasonably common in near expiries just before binary events. For example in a biotech name prior to an FDA decision announcement. If you program in R you can easily see this using the RND package on relevant option chains. Or, for a crude approximation to the risk neutral (implied) density function, plot fly cost vs. log-moneyness.
Yeah, you get some weird data during those events. But I think that's mainly because the IV would be so high, that it screws with prices. That could indeed give you really good risk/rewards on butterflies and callspread and putspreads. But I think the probability curve will still have one top. Do you have an example? Screenshot/graph? I'd like to see that.... Are we talking about the probability distribution right? That has to be within a reason. You can't have an OTM put with a higher probability that the ATM put. The ATM has the highest prob to become ITM vs any OTM's. Or are we talking about the vol-curve? Because that can get out of balance depending on supply/demand... but the prices of options should still be reflecting the probability of becoming ITM, and therefore an option which is further out than another one should always have a lower prob/price...
@Kevin Schmit ... I understand what you're talking about. The bankrupt or triple in value possibility which is quite common in bio-tech and pharmaceuticals. So when the event is coming up, the probability of the stock staying at the current level is actually very small, and either -90% or +200% is quite high. I see that that would mean the distribution could look bimodal.... That could screw up the gamma/theta distribution as well. But I think that's merely a fluke in the pricing models, since delta's will always add up to 100. And call spreads and put spread can never be negative. So in the end... linearity in the payoff would mean you can take advantage of those scenarios... wouldn't you say? It's an interesting subject though.
So for example last summer when home capital (hcg.to) got screwed for over leveraging, the stock went from $30 to $4 a share. If we would look 2 years into the future, the stock would either be 0 or it would recover. Even tho implied vol was high, the 2 year DOTM options don't have that much vega so even with the increased vol, the DOTM were still cheap. So the event was bi-modal (inflection point) but the options market doesn't price in the tails correctly(not enough vega). Is this an inefficiency or am i missing something?
Why are the OTM options not priced correctly? What prices do you see and what would you pay for a 30 call 2 years out?