HighFlyer Stock currently sells for $48.A one-year call option with strike price of $55 sells for $9, and the risk-free interest rate is 6%.What is the price of a one-year put with strike price of $55?
A)$9.00
B)$12.89
C)$16.00
D)$18.72

Question

Quizplus · Accepted Answer

To find the price of the put option, we can use the put-call parity formula, which is: $C + Ke^{-rt} = P + S$, where $C$ is the call price, $K$ is the strike price, $e$ is the base of the natural logarithm, $r$ is the risk-free interest rate, $t$ is the time to expiration (in years), $P$ is the put price, and $S$ is the current stock price. Rearranging the formula to solve for $P$, we get: $P = C + Ke^{-rt} - S$.Given:- $C = $9$- $K = $55$- $r = 6\% = 0.06$- $t = 1$ year- $S = $48$Plugging these values into the formula gives us:$$P = 9 + 55e^{-0.06} - 48$$$$P = 9 + 55 \times e^{-0.06} - 48$$$$P = 9 + 55 \times 0.94176 - 48$$ (using $e^{-0.06} \approx 0.94176$)$$P = 9 + 51.8468 - 48$$$$P = 12.8468$$Rounding to two decimal places, the price of the put option is approximately $12.89.

HighFlyer Stock Currently Sells for $48