Academic researchers are wrong about Volatility Smile. My findings: Volatility Smile is an inherent (built-in) property of options! The academic definition and explanation attempts for Volatility Smile are wrong! B/c it's "very normal and mathem. correct and as well expected", hence inherent. Proof for this claim will be posted here soon... Stay tuned!... (need first to sort my brain after this shocking bombshell discovery I made today... )
I made the discovery while testing a Covered Call strategy: This is the "equilibrium" formula for Minimum Premium one needs in a Covered Call trade to sell a Call option to get a MaxProfit >= 0 (at strike K and higher): MinPremium = StockPrice - Strike Now apply this to a string of Call strikes, and then calc the IV for these Premiums: Off of ATM it will show rising IVs forming the very well-known Volatility Smile! Ie. it's inherent to options; a built-in property of options. Therefore the academic observation/statement "Equity options traded in American markets did not show a volatility smile before the Crash of 1987 but began showing one afterwards" (see above wiki link) cannot be true as it must have been present even before 1987, IMO, though I have no such old historic options data to verify this, but maybe others can check & verify it.
You can take realized price data, and solve for the IV figure at a given past date, that if bought/sold and hedged, would have realized PnL of zero. So you can construct a vol surface where every IV figure is “fair value”, only in hindsight of course. Depending on where you are in strike space, that IV figure won’t be the same at atm. And it won’t always be higher than atm vols either depending on the instrument and where your strike is. Post ‘87 index put skew definitely steepened even though it didn’t always trade completely flat before then. The world isn’t perfectly risk neutral so strategies that draw down during bad macro conditions carry risk premium that is discounted by varying degrees over time. After that catalyst market snapped to new pricing that arguably prices down and out vol more consistently, in a relative fashion to other risk assets, with regards to the skewness of the PnL profile and its convariance with macro conditions. Market still does a weird thing to this day where proper pricing is known by smart money in a certain area but stays dislocated for a while until it rapidly snaps into place on the heels of a known or sometimes unknown catalyst. It’s rare though. Researchers are always behind the ball. They aren’t even playing the game as smart money. Don’t pay too much attention to their commentary aside from a prompt of some potentially useful questions to start thinking about.
@earth_imperator, there has been vol-smiles pre-'87, typically in calls in SN (even index) and since the listing of futures options. Also smiles on index due to lack of spread (NBBO) liquidity, but we await the wisdom of a guy who doesn't understand synthetics.
Grand unified theory of options pricing: a call must be greater than S-K. At that point profit is maximized and infinite gamma is achieved. sle was wrong.
The volatility curve is simply an expectation (IV) of what realized volatility will be once the asset moves towards that region. Obviously if we move down 10%, the realized volatility will be higher, thats why you have the smile. You can read it here.