Question

A put option that expires in six months with an exercise price of $45 sells for $2.34. The stock is currently priced at $48, 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.) Call priceſ

Answer 1

1). According to the Put-Call Parity

Call Price = Put Price + Stock Price - [Exercise Price * e^{-(r * t)}]

= $2.34 + $48 - [$45 * e^{-[0.035 * (6/12)]}]

= $50.34 - [$45 * 0.9827]

= $50.34 - $44.22 = $6.12

2). According to the Put-Call Parity

Put Price = Call Price + [Exercise Price * e^{-(r * t)}] - Stock Price

= $4.20 + [$70 * e^{-[0.04 * (4/12)]}] - $69.80

= [$70 * 0.9868] - $65.60

= $69.07 - $65.60 = $3.47