A shares are trading at $14.90 per share. In four months time, they will pay a 2

Question

A shares are trading at $14.90 per share. In four months time, they will pay a 20 cent dividend. Interest rates (compounded continuously) are 2% per annum. A European put option is trading with strike price $15.50, maturing in 6 months time. (1) If the put option has a price of 63 cents, what is the arbitrage opportunity? (2) A European call option with strike price $15.50 and maturity in 6 months trades at 17 cents. What must the price of the put option be to avoid arbitrage opportunities? How would you trade if the put’s price was $1?

Explanation / Answer

According to Put call parity:

S+P=C+Xe^(-rt)+Present Value of Dividends

=>P=0.17+15.5*e^(-2%*6/12)-14.9+0.2*e^(-2%*4/12)

=>P=0.81

Price of put option should be $0.81 or 81 cents

If it is 0.63 buy put buy stock sell call borrow money

If it is 1 sell put sell stock buy call lend money (or invest at risk free)

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