Assume that a stock’s price over the next two periods is as shown below.

The initial value of the stock is $100. The probability of an up move in any given period is 40%, and the probability of a down move in any given period is 60%. Using the binomial model, the probability that the stock’s price will be $101.20 at the end of two periods is *closest* to:

- 48%.
- 24%.
- 16%.

Answer:

where

n = 2 (number of periods)

**x = 1 (number of up moves: ud and du)**

p = 0.40 (probability of an up move)

p(1)=(21)0.401(1−0.40)2−1=2!(2−1)!1!×0.401×0.61=2×0.40×0.60=0.48

Can somebody help me understand why ‘x (number of up moves)’ is 1?