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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?

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  • $\begingroup$ I imagine it was always there, that was just when it became apparent current models didn't account for it. $\endgroup$ – jeff m Dec 5 '13 at 15:28
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    $\begingroup$ @jeffm Of course you are right, so I am actually asking, when it stopped being neglictible. $\endgroup$ – user40989 Dec 9 '13 at 14:21
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    $\begingroup$ @user40989 can you clarify what you mean by capital markets, if you are excluding equity markets (as your question appears to)? $\endgroup$ – tfb Apr 19 '14 at 17:08
  • $\begingroup$ I remember reading this in the JC hull book everyone reads as an intro - and indeed the wiki article quotes JC hull when making the 1987 statement - it's in the opening paragraph of chapter 19, section 3. $\endgroup$ – will Jan 22 '17 at 22:24
  • $\begingroup$ @jeffm - i'm not sure it was always there - because that's not how the market was being modeled. If the majority of the market participants model the market using model A, then they will pull the traded prices inline with that model. If one way something happens (i.e. 1987 crash) and there is some realization across the market participants that they're modeling it wrong, then they will stop using model A (which in this case does not predict a smile), and move to model B. You see similar discrepancies today where certain products will always be valued using particular models (i.e. SLV vs LV). $\endgroup$ – will Jan 22 '17 at 22:27
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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.

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    $\begingroup$ I have read as much, but can anyone point me to a (commercial ?) source of US options data before 1990, so I see for myself? $\endgroup$ – onlyvix.blogspot.com Jun 5 '16 at 14:11
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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.

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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.

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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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