For a stock price following a binomial process,the up factor U = 1.1,the down factor D= 0.9,the dollar return (1 +R)= 1.05 percent (per period),and the initial stock price is 100.The probability that the stock will have 18 up movements and 2 down movements is:

Question

Quizplus · Accepted Answer

We can solve this problem using the binomial distribution, where the probability of having k up movements in n periods is:

P(k) = (n choose k) * U^k * D^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways of choosing k items from n.

In this case, we want to find the probability of having 18 up movements and 2 down movements in 20 periods, so we have:

P(18) = (20 choose 18) * U^18 * D^2

Substituting the given values, we get:

P(18) = (20 choose 18) * 1.1^18 * 0.9^2 = 0.0669

Therefore, the answer is B.

For a Stock Price Following a Binomial Process,the Up Factor