If the stock price follows a random walk, successive price changes are statistically independent. If σ² is the variance of the daily price change, and there are t days until expiration, the variance of the cumulative price change is A)σ² B)(σ²)× (t). C)(σ²)/t. D)(σ²)× (t²).

Question

Quizplus · Accepted Answer

The variance of the cumulative price change is equal to the sum of variances of each day's price change over the t days until expiration. Since the daily price changes are statistically independent and follow a random walk, the overall variance is equal to the variance of one day's price change times the number of days, which is (σ²)× (t).

If the Stock Price Follows a Random Walk, Successive Price