The day when the markets smiled

Pablo Triana. Professor. IE Business School

3 December 2007

The crash of 87 may have caused a lot of tears, but it also led to a big advance for the finance sector: the “volatility smile”

2007 marks the 20th anniversary of one of the most important developments in finance. One of the most interesting features of the options markets is the so-called “volatility smile”, which shows that traders are inputing a different volatility figure into the pricing formula depending on the option’s strike. The relationship between implied volatility and strikes usually presents a smile-like shape, indicating that those contracts with extreme strike levels (either deep out-of-the-money or deep in-the-money) are assigned larger volatility inputs by traders.

The volatility smile is a relatively recent phenomenon. Barely twenty years old. October 19th, 1987 is conventionally credited as its birth date. It is not too difficult to understand why. That day, when equity markets worldwide plummeted (with the Dow Jones tumbling by almost a quarter, its worst single-day percentage decline ever), market players experienced the first serious crash since the introduction of the Black-Scholes option pricing model in 1973. The first unavoidable wake-up call reminding traders of the unworldly unrealistic assumptions of Black-Scholes when it came to the probability distribution underlying financial markets.

The model assumes that asset returns follow a Normal distribution (thus ruling out the possibility of extreme moves), but clearly there was nothing “normal” about daily market declines of 23% (New York), 15% (Tokyo) or 10% (London). Today´s equivalents of such plunges would be the Dow Jones, the Nikkei, and the FTSE falling by 3200, 2700, and 650 points respectively. Truly monstruous.
The very real encounter with the 87 crash was, for traders, akin to an encounter with a UFO: the awe-striking discovery of something that wasn´t supposed to exist. Once option players saw the UFO almost twenty years ago, there was no turning back. The Black-Scholes radar had to be fixed to account for the possibility of rare events. The model had been hopelessly undervaluing deep out-of-the-money puts. The 1987 crash, by making those puts incredibly profitable for their owners (and incredibly unprofitable for the traders that had sold them), showed this very clearly. Either a substantial premium was to be added on top of the pure Black-Scholes price, or those puts could never be sold again.

As a result of such protective adjustments on the part of dealers, the smile was born. Implied volatility would be manipulated so that the values of options with strikes at the extremes could be significantly pumped up (the higher the volatility input, the higher the resulting option price). Prior to the 87 crash, dealers had been content to charge the same volatility independent of the strike level. The chart plotting implied volatility and strikes was more or less horizontally flat, exactly as Black-Scholes would dictate. After October 1987, such flatness gave way to the more realistic smiling shape.

From the equity markets, the smile expanded. Currency, interest rates, commodity, and other markets soon developed their own grin-like figures. While there are differences between all these markets (they all smile, but “some smile more than others”), the common theme is the same: in all markets, traders feel the need to make adjustments to the model so as to arrive at option values deemed relevant according to the particular real-world realities of the moment. The volatility smile, thus, very graphically exemplifies two key basic ideas: financial markets do not behave normally, and when it comes to option pricing traders are (as they should) fully in charge.

The appearance of the volatility smile has had important ramifications for hedge funds and other punters, essentially affording new ways to make money (as well as the possibility to make more money using old tactics). An obvious way to “play the smile” is through combinations of plain-vanilla options that would generate a mark-to-market gain or loss depending on the future shape of the smile. As the smile changes, the new implied volatilities would yield new option values which would render profits depending on the exact strategy employed.
The smile has also allowed financial players to make more money from a time-honoured tradition, namely options selling. Selling options is a simple way to collect cash fast. It is also a route to the poorhouse were the underlying markets to go crazy, and many prominent players have gone down because of this. But thanks to the presence of the smile, at least the collected premiums (particularly if you sell deep out-of-the-money puts, as is customary) are much tastier than priorly.

Recent developments have added additional ammunition to those willing to generate returns via smile plays. The launch in 2006 of options on the VIX volatility Index (following the launch of VIX futures two years earlier) can allow direct, exchange-based bets on the implied volatilities of a wide range of strikes. And just a few months ago, futures contracts based on two other VIX-like indices began to trade. Fitting commemoration of the smile´s twentieth birthday.


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