One more question re: long term maturities. Assuming the stock returns follow a more normal distribution, what would the IV curve look like in that situation? Just a smile? Eg for the following:
Need to point out something important to you. When you look at the IV skew of the strikes, the shortest months almost always look steeper and more negatively skewed, which often times is the case. But when you compare the IVs of the deltas or standard deviation points across all months on the term structure, often times they are the same or even steeper in the further out maturities. Here are some examples: These were taken live from a product I trade. Notice how the 1st month (purple line) IV puts skew based on delta are relatively the same as the other months. If this was an IV vs strike graph the 1st month skew would be much more pronounced. I don't ever graph or look at the skew based on strike or simple moneyness which most beginners do. It's like comparing apples to oranges. You need to adjust for the time factor between the different maturities. Comparing IVs of the same deltas or sigma points is much more relevant and what most sophisticated option trading desks do. So there you go.
"One more question re: long term maturities. Assuming the stock returns follow a more normal distribution, what would the IV curve look like in that situation? Just a smile?" You would think that would be the case, but in all likelihood, the IBM IV curve would still have been negatively skewed during this period. A couple of reasons. Thanks to the 1987 Crash downside puts will forever trade at a premium to equivalent upside calls. There is simply no shortage of OTM put buyers, which will obviously make the IV curve more negatively skewed for all equity indexes and most individual stocks. The other factor driving the steepness of the equity skew is many people like to sell covered calls against their long equity position. And almost everyone has a long equity position in some shape or form (IRA, 401K, etc.). Another reason for the negative skew is the anticipated behavior of the underlying and realized volatility on declines vs rallies. The stock market tends to grind and trend higher, while the moves lower are often swift melt-downs and filled with gaps. As a result implied volatility tends to creep in on a rally, and explode on a break. That IV behavior is fully priced in on most equity IV curves.
I like the intuition behind this but curious if you have seen any quantitative support of the idea? If so would love to read up on it.
Don’t want to add to the confusion but the important thing to note is that volatility, and hence skew, is a model output. It just helps people speak the same language. You take price (a reality). You take the Black Scholes model (one of many vol models, with many unrealistic assumptions including constant vol). Mix the two and get volatility. It has little to do with realised volatility, and trying to get satisfying physical explanations for skew can be misleading.
I have not seen any quant research to back this up. It's simply one of the stylized facts of the industry. I forgot to mention that another factor driving the low IV of the calls is the popular synthetic collar strategy large institutions implement. This is where against their long equity position a portfolio manager will often purchase protective OTM puts and finance them by selling OTM calls, which steepens the skew even further.
That kind of willful ignorance is just baffling to me. The mentality you're projecting here would lead you to the inescapable conclusion that the Earth is flat and the sun goes around it. After all that's obviously what we see and fuck investigating it further, am I right? Most of us moved into the hypothesis/test concept of the scientific method a few hundred years ago, but some seem stuck in the 1400s. They called it the"dark ages" for a reason! Like I said, it's an interesting hypothesis that could be somewhat easily tested. Why in the world would you be actively against checking to see if anyone had?
At first I thought it was funny to say F'k quant support. But truth be told - at the end of the day it is irrelevant why it is there. All that matters is that it is there and that you trade around it. Speaking anecdotally, paper flow plays an enormous part and the dynamics VST laid out were consistent with what I saw on order flow, time and again. As for flat earth. Ever been to Kansas? End of argument!
I would say don't worry too much on what "they" say. Theres a billion theories on the smile and each trader has to learn to read it and take advantage of it. It allows you to choose the best strikes. This is why options are pure vol really, the strategies themself are constructed to extract alpha within the implied surface. Ratio spreads isolate skewness. Condors and Fly's take advantage of kurtosis. Options use optionality with vol to price market magnitudes. Its the insurance of the markets.