If the stock price follows a random walk successive price changes are statistically independent. If σ2 is the variance of daily price change, and there are t days until expiration, the variance of the cumulative price changes is:
A) σ2
B) (σ2) * (t)
C) (σ2)/t
D) none of the above

Question

Quizplus · Accepted Answer

The variance of the cumulative price changes is equal to the sum of the variances of the individual price changes. Since the price changes are statistically independent, the variance of the sum is the sum of the variances. Therefore, the variance of the cumulative price changes over t days is (σ2) * (t).

If the Stock Price Follows a Random Walk Successive Price