In the previous chapter we looked at the basics behind Black-Scholes for European options. We'll continue to explore options in this chapter and look at volatility and how to use F# to help us out. Volatility measures changes in price as annualized standard deviation, which is the rate at which the price of a financial instrument fluctuates up or down. Higher volatility means larger dispersion and lower volatility means, of course, smaller dispersion. Volatility relates to variance and variance equals the square of the standard deviation, as covered previously.
Black-Scholes assumes normal distributed movements in stock prices, which is not really the case in reality according to observations. In real life, the distribution is more fat-tailed, which means that negative price movements tend to be larger when they occur, but positive movements are more common, and smaller on average.
Figure 1: Courtesy of Yahoo! Finance. Shows S&P 500 Index with low volatility...