Black-Scholes’ Dirty Little Secret

Tuesday, 6 September 2011 19:35 by The Lunatic

Back in 1973, two mathematicians named Fischer Black and Myron Scholes wrote a paper entitled "The Pricing of Options and Corporate Liabilities".  This became known as the “Black-Scholes option pricing model”, which earned them a coveted Nobel Prize in economics in 1997 (technically, Myron Scholes shared the prize with Robert Merton, another collaborator, since Fischer Black had passed away by that time).

The Black-Scholes option model serves as the benchmark for setting the price of a common stock option. All you need to know is the stock price, the strike price of the option, the time left to expiration, the current interest rate, and this tricky little thing called the volatility of the stock.

Ahhh, the volatility. There’s the rub. The volatility of a stock is calculated using an iterative process called a “cumulative normalized distribution function”. Basically, it looks at the variations of a stock’s up and down movement over a certain time period and offers up a percentage of the average movement. The volatility is an absolute measurement, which is different from a stock’s “beta” – the beta is a ratio of that particular stocks’ volatility as compared to the rest of the market, which is actually much easier to measure.

In my definition of volatility, I said that it relies on the variation of a stock price over a certain period of time. But what period of time should you use? One week? A month? Three months? Six months? A year? Maybe two years? The time period that you use can make a huge difference in the value of the option, but there’s no general recommendation for what period to use.

All of the other factors (stock price, strike price, time to expiration, etc.) are quantifiable values that can be specifically defined. The volatility, however, requires a bit of artistic interpretation.  If the stock was highly volatile nine months ago, but is more stable now, then measuring the historic volatility over the last six months is probably a good choice. Or not. More...

Categories:   Economics
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