Calculate the price of a European put option if the price of the equivalent European call option is $1.05 and the share price,exercise price and risk-free rate are $3.00,$2.50 and 10% p.a. ,respectively,given the option has three months to expiry.

Question

Quizplus · Accepted Answer

To calculate the price of the European put option, we can use the put-call parity formula for European options, which is: $P + S = C + Xe^{-rt}$, where $P$ is the price of the put option, $S$ is the current stock price, $C$ is the price of the call option, $X$ is the exercise price, $r$ is the risk-free interest rate, and $t$ is the time to maturity (in years). Plugging in the given values: $S = $3.00$, $C = $1.05$, $X = $2.50$, $r = 10\% = 0.10$, and $t = 3/12$ years (since it's three months to expiry), we get:$$P + 3.00 = 1.05 + 2.50e^{-0.10 \times \frac{3}{12}}$$Solving for $P$, we find:$$P = 1.05 + 2.50e^{-0.025} - 3.00$$$$P \approx 1.05 + 2.45 - 3.00$$$$P \approx 0.50$$Given the options, the closest value to our calculation is $0.49, so the correct choice is A.

Calculate the Price of a European Put Option If the Price