The 1987 stock market crash had its roots in the misplaced faith the finance industry had in the Black-Scholes framework for option pricing. With the Dow Jones plummeting 23% in a single day, Black Monday, as it came to be known, was partly blamed on the failure of computerized portfolio insurance strategies built on the principles of dynamic hedging.

Unlike traditional insurance, portfolio insurance transfers risk from one party to another by selling futures as markets decrease in value. Essentially, an investor buys an index with part of their investment, and a Put option with the remainder, with the balance between the two managed by the Black-Scholes framework.

With its origin in the early 70s, the Black-Scholes equation is a method of arriving at the fair market price of an option, and has defined the course of the last forty years of mathematical finance.

Its popularity with institutional investors meant that by 1987, around $60 billion of equity were protected through portfolio insurance. This, however, was also the genesis of its downfall; portfolio insurance relies on perfectly liquid markets. But when everyone is selling, this isn’t necessarily the case.

The Black-Scholes framework is only valid under normal market conditions. When you need it most – when you really, REALLY need to sell – liquidity dries up like a puddle on a hot day.

Black-Scholes option pricing makes several flawed assumptions

- Stock price volatility is constant over time. This, however, is never the case.
- Stock prices follow a log-normal distribution. This dramatically underestimates the effect of the low probability, high impact events that occur in reality. This also presuposses that stock prices are as likely to go up as they are down.
- The entire market is assumed to be so large that the actions of traders has no effect.
- The risk-free interest rate is constant. Again, this isn’t the case
- Stocks are priced continuously. But in reality, they’re priced in small steps.

Despite these assumptions, Black-Scholes grew in acceptance. By 2006 over $400 trillion worth of securities were priced by methods inspired by the Black-Scholes method. Let me emphasize one important point – this tremendously large sum of money was tied up in derivatives because the of the excessive confidence the finance industry had in Black-Scholes.

The theory has, however, vocal detractors. Nassim Taleb, a trader who profited from the 2008 subprime crisis, says that Black-Scholes is essentially an economic “argument to make a well known (and used) formula compatible with the economics establishment”, rather than a model”. A paper by Taleb and Haug describes Black-Scholes as “academic marketing exercise”, and accused Myron Scholes, one of the two responsible for the Black-Scholes model, of precipitating the subprime crisis.

Black Monday and the subprime crisis certainly originated in the excessive confidence people had in flawed mathematical models based on the spirit of Black-Scholes. But I’d like to lay the blame at least partly on greed. Black-Scholes simply provided a petri dish for simple human avarice to thrive.

The BS options pricing formula works pretty well; about as well as classical mechanics does in describing the velocity and position of baseballs. Does classical mechanics describe quantum effects? No, not really, but those were poorly understood when classical mechanics was developed. Similarly for BS – it didn’t account for all types of risk, but not all of those risk factors had manifested in 1973.

Blaming Scholes for the sub-prime crisis is ridiculous – akin to blaming Niels Bohr for the atomic bomb that leveled Hiroshima.