Question

You gather the following information from the Wall Street Journal: Intel’s stock is selling for $13.50, the risk-free rate is 4% and a put option on Intel is selling for $4.00 matures in one year and has an exercise price of $15.

a) Calculate the equilibrium value of a call option on Intel that has an exercise price of $15 and matures in one year.

b) Assume the Call option is selling for $4.00, create a pure arbitrage.

Answer 1

ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

As per put-call parity

P+ S = present value of X + C

P= value of put option.

S= current price of the share

X= strike price

C= value of call option.

Present value of X = X/e^r

r = risk free rate.

Given:

P= value of put option = 4

S= current price of share=13.50

X= strike price = 15

Present value of X = 15/e^0.04

r = risk free rate. 4%

4+15 = (15/e^0.04)+C

C= 4.59

Value/Price of call option =$4.59

b. If the value of the call option is $4.59, then put-call parity is violated as the actual call price is $4.

And there is an arbitrage opportunity.

Arbitrage strategy:

Buy Call

Buy Risk-free Asset

Sell Put

Sell Stock

Arbitrage profit = 4.59-4 = $0.59