Formula One Racing

1. 4 Flaws of the Black – Scholes Model

“On February 20, 2000, at the very peak of the Fantastic Bubble, the Public Broadcasting System aired a program on ‘The Formula the Shook the World’, describing the Black-Scholes Model as ‘a mathematical Holy Grail that forever altered the world of finance’ and cited an economist who ‘likened the impact of the discovery of the Black-Scholes Formula to that of the discovery of the structure of DNA. ”

The Black – Scholes model, but, was laced with unrealistic assumptions and significant flaws:

· Perfect markets – The markets were presumed to be extremely deep so that the traders  actions could not influence prices.

· Price variations follow a log – normal distribution. If this was right, extreme price fluctuations would nearly never be observed. For instance, the stock market crash of  1987 would have been extremely unlikely to occur if price fluctuations truly followed  the log normal pattern.

· A constant, risk – free interest rate available as a benchmark. The interest rate on small term U. S treasury bills was generally assumed to represent the risk – free rate  needed by the model. But, this rate is never constant.

· Volatility in stock prices that is constant during the life of an option. In real markets, but, stock volatility is never constant, and without a constant volatility factor, the Black – Scholes model simply does not work.

· No risk operations, continuous pricing, perfect order execution. Organised securities  exchanges do not have continuous pricing, but trade in discreet jumps called ‘ticks’ , as prices fall, these ‘ticks’ become proportionately larger. All markets have operational risks and order execution is never perfect.

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