Question

Consider a European call option and a European put option on a non dividend-paying stock. The price of the stock is $100 and the strike price of both the call and the put is $104, set to expire in 1 year. Given that the price of the European call option is $9.47 and the risk-free rate is 5%, what is the price of the European put option via put-call parity?  

Answer 1

Calculation of European put option via put-call parity:  

Formula for put call parity :

C + PV (S) = P + MP

where, C = price of call option

PV(S) = present value of strike price

P = price of put option

MP = market price of stock

Given,

price of call option = $9.47

Strike price = $104

Risk free rate = 5%

Present value of strike price(PV) = $104/1.05

= $99.047

Market price = $100

substituting above values in formula

C + PV (S) = P + MP

$9.47+$99.047 = P + $100

$108.517 = P + $100

P = $108.517 - $100

P = $8.517

Therefore, price of European put option = $8.517