If the stock price follows a random walk, successive price changes are statistically independent.If σ 2 is the variance of the daily price change, and there are t days until expiration, the variance of the cumulative price change is
A)" σ 2"
B)" (σ 2 ) × (t). "
C)" (σ 2 )/t. "
D)" (σ 2 ) × (t 2 ). "

Question

If the stock price follows a random walk, successive price changes are statistically independent.If σ 2 is the variance of the daily price change, and there are t days until expiration, the variance of the cumulative price change is
A)" σ 2"
B)"  (σ 2 ) × (t). "
C)"  (σ 2 )/t. "
D)" (σ 2 ) × (t 2 ). "

Quizplus · Accepted Answer

The variance of the cumulative price change is equal to the sum of the variances of the individual price changes. Each daily price change has a variance of σ^2S1U1P1/2S1S1P0. There are t days until expiration, so the total variance of the cumulative price change is t times the variance of the daily price change. Therefore, the variance of the cumulative price change is S1U1B0S1U1B1 S1U1B0S1U1B1(σS1U1B02S1U1B1) × (t).S1U1B0.

If the Stock Price Follows a Random Walk, Successive Price