The Day When Black Scholes Made Black Scholes
Posted At : August 2, 2007 1:02 AM | Posted By : Pablo Triana
Related Categories: Black-Scholes
The 1987 stock market crash highlighted the structural flaws of the model but it also unveiled its usefulness.
Imagine that you turn on the tv to check the latest news. Instantly, you feel the fear creep up inside. You turn sweaty and white-faced, still not quite comprehending what the little box at the bottom-right of the screen is displaying. Such anguish, though, would be fully understandable. WWIII it may not be, but a drop in the Dow Jones of 3000 points would surely qualify as a terrifying sight.
To the untrained eye, this fictional story seems way too fictional. After all, the market simply can´t tumble by 25% on a single day, right? Well, yes it can. In fact, a meltdown of such gigantic proportions already happened not so long ago. Only twenty years ago, to be exact. By the close of business on October 19th 1987, the Dow Jones had fallen by almost 23%. âBlack Mondayâ was even graver in other parts of the world, with downfalls of close to 50% in some cases.
The October 87 crash is now part of financial markets legend. It was particularly important for the options markets. Bluntly stated, the crash showed that the Black-Scholes pricing model is wrong but it also motivated traders into showing why the model can be vastly useful. In effect, a Black-Scholes-demonizing event showed how reliable Black-Scholes can be in real-life.
As it is well known, so-called portfolio insurance strategies (which were heavily employed at the time of the crash) have been widely blamed for at least accelerating the market´s meltdown on that fateful Monday. Portfolio insurance was an attempt to synthetically replicate a short equity put position via Black-Scholes-inspired dynamic hedging techniques (which are, of course, at the very heart of the model´s machinery). Thus, as Black-Scholes dictates, insurers would sell the underlying when the market fell and would have to buy when it rose. Assuming that the underlying assumptions of perfect liquidity and continuous trading held, one could build a synthetic put in this manner, and in principle be protected from a market downturn.
As the stock market embarked on a bull run at the beginning of the 80s, portfolio insurers would have been forced to follow the herd upward. As the size of the portfolio pool being dynamically âprotectedâ grew significantly, the required buying would have become larger and larger. Portfolio insurance, thus, quite likely provided a non-irrelevant push to the bullish market.
When the severe correction began to take place in mid-October 87, portfolio insurance-motivated selling helped drag the market to unknown depths (in terms of daily negative returns). Trading became illiquid and discontinuous and dynamic hedging inevitably broke down.
Many âinsuredâ parties ended up with no protection from the ensuing mayhem. The crash (which could well be seen as Black-Scholes-inspired) thus unequivocably showed that the model is built on shaky foundations. In the real world, perfectly-replicating dynamic hedging is merely an illusion.
But at the same time, something funny happened as a direct result of the crash. The currently ubiquitous volatility smile was born, a reflection of freshly-developed crashophobia on the part of traders. After witnessing the massacre, it became clear to options pros that markets cannot be assumed to behave ânormallyâ (as the mathematics behind Black-Scholes assume) and that rare events do happen and can be truly criminal. Traders realized that they had been hopelessly undervaluing crash-protecting out-of-the-money puts.
To correct for the mathematical insanity of Black-Scholes, now only too obvious, implied volatility was manipulated upwards so that the values of options with strikes at the extremes could be significantly pumped up, giving birth to the smile. Prior to the 87 crash, dealers had been content to charge the same volatility independent of the strike level, and the chart plotting implied volatility and strikes was more or less horizontally flat, exactly as the âpureâ version of Black-Scholes would dictate. After a 20-sigma event in Wall Street option pros decided to change tact and take protective measures. The smile became such protection, and very graphically illustrated Black-Scholesâ number one comparative advantage, the real reason why it is embraced: a built-in self-correcting mechanism that very easily lets users correct for any theoretical nonsense and deliver reliable outputs. Conveniently allowing traders to adapt the model to real-world realities, Black-Scholes proved its practical worth.
In sum, the same event that highlighted the untrustworthiness of the model (which internal mechanics, arguably, contributed to the event taking place in the first place) helped underscore the reasons for its wild popularity. By producing the volatility smile, traders effectively rescued Black-Scholes from its self-dug graveyard.
