A put option that expires in six months with an exercise price of $45 sells for

Question

A put option that expires in six months with an exercise price of $45 sells for $4.25. The stock is currently priced at $41, and the risk-free rate is 3.5 percent per year, compounded continuously.

What is the price of a call option with the same exercise price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

What is the price of a call option with the same exercise price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Explanation / Answer

Price of the call option:

Put Call parity

S+P =Ee^-Rt +C

S=Current price of stock=$45

P = Put price=$4.25

E = Exercise price=$45

R = Risk free rate = 3.5%

t = time period = 6 months

C = Call price

$41+$4.25 =$45e^-(0.035)(6/12) +C

$45.25 =$45*0.9827+C

C = $1.0285

Call Price is $1.0285

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