Lapel Inc.stock price is $32.00.Joe bets Sarah that the price will be above $35.00 in 6 months (180 days).The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%.If Joe wins the bet,he wishes to be paid with one share of stock.What is the value of the wager to Joe?

Question

Quizplus · Accepted Answer

To calculate the value of the wager, we need to use the Black-Scholes formula:

d1 = [ln(32/35) + (0.05 + 0.25^2/2)*0.5]/(0.25*√0.5) = -0.8528
d2 = d1 - 0.25*√0.5 = -1.2663

N(-d1) = N(0.1856) = 0.5714
N(-d2) = N(0.1056) = 0.5424

The value of the wager is the difference between the expected value of the stock and the price Joe is willing to pay:

value = S*N(d1) - Ke^(-rt)*N(d2) = 32*0.5714 - 35*e^(-0.05*0.5)*0.5424 = $12.44

Therefore, the best choice is C, $12.44.

Lapel IncStock Price Is $32