Question

You are considering purchasing a put option on a stock with a current price of $54. The exercise price is $56, and the price of the corresponding call option is $4.05. According to the put-call parity theorem, if the risk-free rate of interest is 5% and there are 90 days until expiration, the value of the put should be

Answer 1

Given,

Stock = $54, Call = $4.05, Exercise price = $56, Risk-free rate = 5%, Time = 0.24657 [90 365]

The put-call parity formula is C + Ke^-rT = P + S₀ where:

C = Call Price, K = Exercise Price, r = Risk-Free Rate, T = Time to Expiration, P = Put Price, and S₀ = Stock Price

Subtracting S₀ from both sides, we get

P = C + Ke^-rT - S₀

P = 4.05 + (56.00)e^{(-0.05)(0.24657)} - 54.00

P = 4.05 + (56.00)e^-0.0123285 - 54.00

P = 4.05 + (56.00) (0.9877) - 54.00

P = $5.36

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