Question

A stock is currently selling for $79 per share. A call option with an exercise price of $83 sells for $3.95 and expires in three months. If the risk-free rate of interest is 2.8 percent per year, compounded continuously, what is the price of a put option with the same exercise price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer: $7.37

Step-by-step explanation:

The price of a put option with the same exercise price would be calculated as:

C + Xe^-rt = P + S

It should be noted that in the formula above,

P = Put option price

C = price of call option

S = stock price

X = exercise price

r = interest rate

t = time

We then slot in the values which will be:

= 3.95 + 83e^-2.8% × 3/12 = P + 79

P = 3.95 + 83e^-2.8% × 3/12 - 79

P = 3.95 + 82.42 -79

= $7.37