The price of a European call option on RBC stock with an exercise price of $85 and one year to expiry is trading at $3.15.The current price of the stock is $81.25,and the risk-free rate is 2.5%.With no arbitrage,what must be the price of a European put on RBC with an exercise price of $85?
A)$4.83
B)$3.15
C)$1.47
D)$4.71
E)$2.59

Question

Quizplus · Accepted Answer

To find the price of the European put option, we can use the put-call parity formula for European options, which is: $C + Ke^{-rt} = P + S$, where $C$ is the call price, $K$ is the exercise price, $r$ is the risk-free rate, $t$ is the time to expiry, $P$ is the put price, and $S$ is the current stock price. Rearranging to solve for $P$, we get $P = C + Ke^{-rt} - S$. Plugging in the given values: $P = 3.15 + 85e^{-0.025} - 81.25$, which calculates to approximately $4.83, hence option A is correct.

The Price of a European Call Option on RBC Stock