Question

The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to 536 or fall to $26. Assume the risk-free rate is zero. What is the risk-neutral probability of that the stock price will be $367

Answer 1

Let the required probability be p. So, the probability of the stock falling to $26 will be 1-p. So, the expected stock price today will be the weighted average according to the probabilities in the future. Hence,

36 x p + 26 x (1-p) = 30.

10p = 4

p = 0.4.

Answer 2

Let the required probability be p. So, the probability of the stock falling to $26 will be 1-p. So, the expected stock price today will be the weighted average according to the probabilities in the future. Hence,

36 x p + 26 x (1-p) = 30.

10p = 4

p = 0.4.