Onions, Smiles and Anti-Volatility
Team Latte
Apr 5, 2005
In 1973, when some of us were in our diapers and some were unborn Fisher Black, Myron Scholes and Robert Merton started a quiet revolution in Finance. They quietly, yet abruptly changed the landscape of the finance theory and put us all in the quest for that quintessential quasi-asset that we call options. A boring and dull landscape suddenly became alive with heat equations, probability theory and stochastic calculus and a new science was born. To be fair, of course, this revolution was started quite a few years before Black and Scholes by Harry Markowitz and Alexander Sharpe but Black and Scholes's work romanticized this whole revolution and formally ushered in the new age.
Today we have come a long, long way from Black-Scholes.
These days PDEs and Feynman-Kac solution are commonplace in derivatives valuation models used by quants; and though it took the genius of Feynman to pen them down in Physics, these equations appear to be almost trivial in the quant parlance in banks and financial institutions.
Physicists and Mathematicians on Wall Street and the City of London are busy unraveling the elementary particles of derivatives and writing the unified field theory of Finance and traders and structurers in banks are busy churning out ever more complex and esoteric products by the week.
You certainly have heard of Bemudan options, Asian options, Parisian option. But have you heard of Onion options? Well, there is something called an onion option which has got nothing to do with onions - just as Asian options have nothing to do with Asia - but is actually a form of digital options.
These days all option traders smile - well, the client normally cries - and without smiles all their pricing models would be worth a naught. There is so much fuss about smile that you would wonder how the hell did Black and Scholes miss the smile when this dude next to me knows all about it? But can anyone truly capture the smile?
We are living in an era - if you can call a year and a half an era - of low volatility. It is such a pleasant surprise to see volatilities hit rock bottom after turbulent years of late nineties and early this century that some option traders are now getting bored out of their wits. Some of us are familiar with the low vols in the Euroyen futures markets in the early nineties and you may have read about the story of degenerate assets in the Eurodollar futures market in Taleb's excellent book Dynamic Hedging. Degeneracy is caused when volatility approaches zero.
But can volatility ever be negative? That is simply absurd! But in the world of physics there is something called anti-matter which is opposite of matter. Take matter, change the sign and we get anti-matter. Then why can't we have anti-volatility, or negative volatility? Well, we don't have an answer to that, but as we have said, someone may have something to say about this seemingly absurd but fascinating issue as well.
  
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