Suppose a stock is currently trading for $23,and in one period it will either increase to $30 or decrease to $20.If the one-period risk-free rate is 5%,what is the price of a European put option that expires in one period and has an exercise price of $25?
A)$2.79
B)$2.50
C)$2.38
D)$2.21
E)$2.66

Question

Quizplus · Accepted Answer

To calculate the price of the put option, we need to use the risk-neutral probabilities. Let p be the probability of the stock increasing and (1-p) be the probability of it decreasing. We can set up the following equations:
(1+r)f = pfu + (1-p)fd
(1+r)25 = p(30-25) + (1-p)(25-20)
(1+r)25 = 5p + 20
p = (25-r)/5
If the stock increases to $30, the put option will not be exercised, so its payoff is 0. If the stock decreases to $20, the put option will be exercised and its payoff is $5. Using the risk-neutral probabilities, we can calculate the expected payoff of the put option:
Expected payoff = p(0) + (1-p)($5/(1+r)) = (1-p)(5/(1.05))
The price of the put option is then:
Price = Expected payoff/(1+r) = (1-p)(5/1.05)/(1.05) ≈ $2.79. Therefore, the best choice is A.

Suppose a Stock Is Currently Trading for $23,and in One