You have two parts to your question. One is why skew exists and another is about wing option valuation. First part is because of both regulatory pressure and demand for the product when all the correlation is going towards one. Your valuation of wing option is only considering parallel shift of the curve. Imo, for wing option you need to incorporate skew-vega to account for rotation of vol curve
Could you please elaborate on the first part? I lost you there. What do you mean with regulatory pressure and what you mean with correlation towards one? Correlation between what?
Capital adequacy limit imposed by Basel III. @sle explained better here https://www.elitetrader.com/et/thre...h-40-57-days-left.300053/page-15#post-4293883 Regarding correlation, I meant correlation of risk assets during crash scenario. Most of the risk assets go down at the same time during crash
I said that skew exists because of the path dependency of the vol payout. The market expects higher realized vol at lower spot levels and lower realized vol st higher spot levels. Put gamma is maximized at lower spot levels and so the puts benefit more from the higher realized vol (at the lower spot levels) than the call (whose gamma has diminished). In commodities, you are right because that increased vol is expected in either direction and so you get a smirk. In your words, the extreme events (high volatility in the path dependency world) in equities are generally only on the downside. So we were saying the same thing.
While those may apply to some instruments some of the times it certainly is not the main reason for the existence of the skew.
"The market expects higher realized vol at lower spot levels and lower realized vol st higher spot levels" Relative to what? And that is not accurate, the market prices both wings higher relative to what is implied by the assumed distribution used in the pricing model used to convert between implied vols and prices. At least in index options and many other options as well most of the time. And the simple explanation is that extreme events happen more often than implied by the simplified model. Why using a simplified model in the first place then when we all know it's inaccurate? Because the math is so simple to work with. Not sure why you argue with gamma the entire time when explaining what a smile isand why it exists. I recommend a quick review of Heard on the Street and Basic Black Scholes, both by Falcon Crack. He has a talent for explaining complex things in simple ways. I am not trying to be condescending just saying that OP asked for a simple explanation, why not delivering one?
Relative to ATM vol (which is what you kind of expect the underlying to realize). In US equities, the market does not price the upside higher than the ATM (with some few exceptions which are where the market projects higher realized vol if the spot gets to that level (like a takeover event or some momentum names). In Asia equity options, skew is flatter, but that has to do with a vibrant structured products market which keeps the downsides offered. In other asset classes, you are right: the wings on both sides price higher. I gave a straightforward explanation consistent to the OP's understanding of options. You talked about Pareto distributions.
I referred indirectly to normal and log normal distributions. Aside that the explanations seem to slowly converge. ;-)
Thanks guys, this has helped alot. I am summing it up as - the variance of gamma + the path dependency of vol is what causes the skew. When the underlying trades lower, not only are we expecting higher realized vol but those options will now also have higher gamma. So this brings me to the next question, how to value skew? Most (if not all my skew trades) are based on what is usually implied vs what is currently implied and what the underlying distribution has realized in the past. Let's say (using the original example with SPX), spx realized 6 month daily skew is -3 + implied skew has had a range between 3-8 over the same time period. NOW it has a skew of 10. Would this look like a time to put on a vega weighted short back spread? This however does not incorporate the path dependency of gamma. Should I be bringing the local vol model into play to help me with that? Ps. Has anyone traded 10+ strikes on a not so liquid underlying (5000> daily contracts) to replicate a varwap?
https://www.jstor.org/stable/pdf/2329066.pdf?refreqid=excelsior:0520aed7748291ef1f58b5d84bc5e454 I am finding the paper to be an interesting read. Maybe xGARCH news impact curves can be used to help value the skew. Thoughts?