Random Walks and Volatility So to statistically describe movements of stock price, you model the price (technically its logarithm) as a function of time as a random walk. If the mean of the price doesn't change over time then the variance in the stock price is proportional to time: $$\langle (p(t)-p(0))^2 \rangle = \nu^2 t$$ (2.16) Here $p(t)$ is the price of the stock (really is log) as a function of time $t$. This as we've seen is proportional to the number of steps taken, which is also proportional to time. What's the constant $\nu$? That depends on the stock. Some stocks have a high "volatility", that is the prices go up and down quickly, while others have a low volatility, they're not expected to change much over time.