Written by: Anonymous

The greatest trick the devil ever played was convincing the world that he didn't exist.


It has taken me some time to get back and discuss the hazards of the proliferation of derivatives. I apologize.

I had an interesting conversation today with a professor of finance here at bravo-school that prompted me to sit down and hammer out what I wanted to discuss.

First, a fact: the figure that enjoys the greatest level of acceptance in the financial community for notional value of derivatives outstanding is $71.1 trillion - a little less than 7X our GDP.

The pricing of these instruments, i.e. options, is predicated upon option pricing models, of which there are numerous varieties. A majority of these models are modifications of two types: the Black-Scholes-Merton Model and the Binomial Model. We will not spend anytime on the intricacies of these models, but discuss a singular certain assumption that all of the existing models, be it a version of one of the two listed or something all together different, share.

And that is the idea of price continuity.

Price continuity assumes 1) that there will always be a price and 2) that the next price will not deviate materially from the preceding price.

In the world in which we live, i.e., in the deep fat of the normally distributed curve where 95% of *all* possibilities occur, in the world of two-sigma, price continuity is not an assumption, but by and large, a fact. Option-pricing models and their extensions, i.e. hedging models, work. (I will not discuss here the menacing assumption of constant volatility or that historical volatility is an adequate proxy for future vol.)

But lets talk about things three-sigma. Like a hurricane in far southern-Atlantic that makes landfall in Brazil, or, for that matter, 9/11.

As an asset prices over time, moves are reasonable, and easy to hedge. But if an asset prices outside two-sigma, e.g. the Rubble in 1998, there may simply be no price. (On 9/14/01, when trading at the NYSE resumed, thirty minutes after the exchange opened, the specialists at the American Express booth still could not open the stock, a Dow 30 issue. The bid, i.e. the highest willing price to be paid for the stock, was some 10% below its previous close and current offer. There was no price continuity for one of the exchange's most liquid issues)

When there is no price, there is no ability to trade out of a position. Furthermore, hedging 'directives' from models, which come at you in spades as assets price "rapidly", are unable to be executed.

Terminally, any model is only as good as its assumptions. Deep within the $71,000,000,000,000 worth of derivative contracts is the assumption of price continuity. Faith in the efficiency of markets is the crutch upon which all the actors who require the perseverance of price continuity reside. Markets are efficient within two-sigma. Markets become multi-modal mobocracies outside of two-sigma - and price continuity is the daily yield of a unicorn hunter. And the market inefficiency that is a result of the assumption of price continuity will beg resolution by radical means.