Question

A one-year European call option on Stanley Industries stock with a strike price of $55 is currently trading for $75 per share. The stock pays no dividends. A one-year European put option on the stock with a strike price of $55 is currently trading for $100. If the risk-free interest rate is 10 percent per year, then what is the current price on one share of Stanley stock assuming no arbitrage?

Answer 1

Strike Price = X = $55, Price of call option = call premium = c = $75, Price of put option = put premium = p = 100,

Risk free rate = r = 10% per year, No of years = T = 1

Let S = Current price of stock of one share

We know that according to no arbitrage condition of put-call parity,

S + p = c + X / ( 1+ r)^T

S + 100 = 75 + 55 / (1 + 10%)¹

S + 100 = 75 + 55 / 1.10

S + 100 = 75 + 50

S = 75 + 50 - 100 = 25

Hence current stock price of one share = $25