Question

# Consider a European call option and a European put option on a non dividend-paying stock. The...

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?

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

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