In a one-period binomial model, assume that the current stock price is $100, and that it will rise to $110 or fall to $90 after one month. If an investment of a dollar at the risk-free rate returns $1.001668 after one month, what is the standard deviation of monthly stock return under the risk-neutral probabilities?
A) 9.93%
B) 9.97%
C) 10.00%
D) 20.00%

Question

Quizplus · Accepted Answer

Using the formula for the risk-neutral probabilities, we have:
p = (1 + rf - d) / (u - d) = (1 + 0.001668 - 1) / (1.1 - 0.9) = 0.0834
q = 1 - p = 0.9166

The expected stock price after one month is:
E(S) = pu + qd = 0.0834 x 110 + 0.9166 x 90 = 91.68

The standard deviation of the stock return can be calculated as:
σ = sqrt[pq(u - d)^2 / 1] = sqrt[0.0834 x 0.9166 x (110 - 90)^2 / 1] = 10.00%

Therefore, the answer is choice C.

In a One-Period Binomial Model, Assume That the Current Stock