Volatility Smiles: Market History, Quoting Effects, and Model Dependence
Summary
The document asks when volatility smiles began appearing in capital markets, especially around the 1987 equity crash. Responses offer several different perspectives rather than a settled account. One says smiles became visible in equities after the crash and later appeared in foreign exchange and other markets; another recalls early 1990s yen-denominated products and subsequent spread to other major currencies. A respondent who searched the literature could not identify the first publication.
Other replies dispute whether the smile has a single historical starting point. They describe implied volatility differences across strikes as potentially shaped by option tick sizes, demand for low-probability tail payoffs, and the mismatch between market prices and models such as Black-Scholes. One response calls the smile an artifact of measurement, while another emphasizes behavioral demand. These are claims in a discussion, not evidence resolved by a systematic dataset or cited chronology, so the document leaves both the origin and explanation uncertain.
Key ideas
- The replies associate visible equity volatility smiles with the period after the 1987 crash and mention later observations in other markets.
- One recollection places early smiles in yen-denominated products in the early 1990s, but the discussion establishes no definitive first appearance.
- Option price increments may affect implied volatilities for very low-priced tail options.
- Demand for unlikely outcomes and model mismatch are offered as possible explanations for smile patterns.
- The competing explanations are not reconciled with systematic evidence in the document.
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Full text
# When did volatilities start to smile in capital markets? # When did volatilities start to smile in capital markets? Glimpsing through literature, I read that volatilities in the equity market started to display a smile after the crash in 1987. But when did volatilities start to smile in capital markets? ## Answer by Chris Andy (score 1) https://quant.stackexchange.com/a/25853 From the information I've gathered the volatility smile concept did not exist prior to 1987. Since then it can be seen in foreign exchange markets and various other investments. Equity derivatives show volatility pairs and the smile tends to seen quite easily here. ## Answer by JoshK (score 0) https://quant.stackexchange.com/a/31639 I'm going to question your initial assumption. The volatility smile is always there. Ultimately all the volatility smile means is that low probability payout options imply a higher volatility than higher probability ones. Simple example being the AAPL 10000 call will imply a higher vol than the AAPL 100 call. There is an intuitive mechanical reason why this HAS to be. Many of the out of the money options are worth something like .00001. But generally they will have to be quoted and trade in some increment like .01 or .05. So just market structure (for listed options) will force some kind of minimum price - and that's more than the ATM vol justifies. But more importantly, as people we always worry too much about low probability events. We pay too much for lottery tickets, we agree to settle cases that we know we should win, etc. All that behavioral stuff that has been true since the dawn of time. That drives people to price up a little bit the tails for options. Just imagine telling your boss that you sold the AAPL 300 call JAN 18 for .005. "But I sold it for an iVol of 25!" No, you would just get fired. ## Answer by Dave Harris (score -1) https://quant.stackexchange.com/a/31300 If you mean when did it appear in the literature, I did research on it and found 3800 articles on it and never did get back to the first one. If you mean when did it first appear in the data, I also did a population study of the CRSP universe. It is an artifact of the model and is a result of the model being mismatched with reality. The "smile" is an artifact of measurement. You can actually show that Black-Scholes and related models are "inadmissible," statistical solutions. I just did a presentation on this for a math group, though not this specific problem. It was a simpler coin toss or roulette style problem that induced the same type of effect. I was inspired by a cunningly simple problem by Parmigiani and showed how changing your statistical axioms and following them blindly, which we do with automated or big data solutions, led to very, very different results using the theoretically valid results under different systems of axioms. I have a set of papers that I am presenting at conferences that covers how the empirical problems with Black-Scholes and Ito calculus style models comes from misunderstanding the deeper axiomatic structures and how to fix them. There is actually an early warning by von Neumann and Morgenstern in a footnote in a work that preceded Black and Scholes work, but it was never heeded. Things like the smile are empirical contradictions and nature cannot have those. When you see them, something else is going on. In this case, it is an accident of how it is being looked in the frame of a model. Change the frame and the problem vanishes. ## Answer by Atlas (score -2) https://quant.stackexchange.com/a/9636 I recall Rebanato in Volatility & Correlation mention early 90's in Yen denominated products and rapidly being adopted for the other majors. Sure there was money to be made doing these skew trades but markets in both volatility and the underlying were quite possibly truck wide.
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