Question

A stock is currently selling for $81 per share. A call option with an exercise price of $83 sells for $4.05 and expires in three months. If the risk-free rate of interest is 3 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.)

Put price $

Answer 1

Using put call parity:

Given stock = 81, call = 4.05, exercise = 83, riskfree = 3, t = .25, calculate put

The put-call parity formula is C + K*(e^-rT) = P + S

where: C = Call Price, K = Exercise Price, r = Risk-Free Rate, T = Time to Expiration, P = Put Price, and S = Stock Price

Subtracting S from both sides, we get P = C + Ke-rT

Plugging in our known values, we have:

P = 4.05 + (83.00)e(-0.03)(.25) - 81.00 P

= 4.05 + (83.00)e-0.0075 - 81.00 P

= 4.05 + (83.00)0.99252805481914 - 81.00 P = 4.05 + 82.379828549988 - 81.00

P = $5.4298 or $5.43