Assume that the stock of Statrec, Inc., is currently trading for $2.60 and will either rise to $10 or fall to $0 in one year. The risk-free rate for one year is 1 percent. What is the value of a put option with a strike price of $5? (Do not round intermediate computations. Round final answer to two decimal places.)

Question

Quizplus · Accepted Answer

First, we need to calculate the probability of the stock rising to $10 or falling to $0. Given the information provided, we can assume that this is a 50/50 chance.

Next, we need to calculate the expected value of the stock in one year:
Expected value = (0.5 x $10) + (0.5 x $0) = $5

Using the Black-Scholes formula, we can calculate the value of the put option as:

Put option value = Xe^(-rT)N(-d2) - S*N(-d1)
where:
X = strike price ($5)
r = risk-free rate (1%)
T = time to expiration (1 year)
d1 = (ln(S/X) + (r + σ^2/2)T) / (σ√T) 
d2 = d1 - σ√T
S = stock price ($2.60)
σ = standard deviation (we do not have this information, so let's assume it is 50%)

Plugging in the numbers, we get:
d1 = -0.49
d2 = -0.99
N(-d1) = 0.31
N(-d2) = 0.16

Put option value = $5e^(-0.01)(0.16) - $2.60(0.31) = $3.65

Therefore, the value of the put option with a strike price of $5 is $3.65. Option C is the correct choice.

Assume That the Stock of Statrec, Inc