Black-Scholes and algorithms

Trading and risk have always been intertwined, with merchants constantly seeking ways to reduce their exposure to unforeseen events. As the Dutch Golden Age of the 17th century began, merchants in Amsterdam and Antwerp began using options – which gave the holder the right to buy or sell a security at a set price – as an insurance. Similar products such as warrants were traded on stocks in Wall Street in the 1920s, but were never “mathematically” priced.

That changed in 1973. Two US academics, Fischer Black and Myron Scholes, backed by a third, Robert Merton, published a paper that contained a model to calculate fair market value for call options. It gave traders a supposedly objective method of comparing option prices.

Two years earlier, US president Richard Nixon had removed the ability to exchange the dollar into gold, ending the international system of fixed exchange rates. Less than two years later, the world would be dealing with inflation triggered by oil price shocks. The accompanying interest rate volatility meant investors needed to hedge their risk, and led to a demand for more options and other derivatives.

In the following decade, futures and options, at one time used by farmers to lock in the price of physical commodities, increasingly became used for financial products.

Volumes exploded. But the significance of the formula has been hotly debated. Some ask whether it is really possible to calculate the “true” price or value of any object.

The biggest blow came in 1997 with the failure of Long-Term Capital Management, the hedge fund that had Merton and Scholes on its board. The fund had spectacular early returns. But the unexpected Russian sovereign default in 1998 upset its calculations and it needed a bailout from the Federal Reserve after it lost $4.6bn in a matter of months.

In a 2008 paper, Espen Gaarder Haug and Nassim Nicholas Taleb argued that Black and Scholes only came up with a theoretical argument built on a new way of “deriving” the 1900 formula of Frenchman Louis Bachelier.

Philip Stafford