Options, Futures, and Other Derivatives, 10th Edition

15.4 VOLATILITY

The volatility, σ, of a stock is a measure of our uncertainty about the returns provided by the stock. Stocks typically have a volatility between 15% and 60%.

From equation (15.7), the volatility of a stock price can be defined as the standard deviation of the return provided by the stock in 1 year when the return is expressed using continuous compounding.

When Δt is small, equation (15.1) shows that ${\sigma }^2\text{ Δ }t$ is approximately equal to the variance of the percentage change in the stock price in time Δt. This means that $\sigma \sqrt{\text{ Δ }t}$ is approximately equal to the standard deviation of the percentage change in the stock price in time Δt. Suppose that $\sigma \text{ = 0}\text{.3}$, or 30%, per annum and the current stock price is $50. The standard deviation of ...