Put Call Parity

(a)The continuously-compounded risk free rate per annum is 20% per year. European call options on the stock of XYZ CORP with an exercise price of

$35 and a maturity date 6 months hence are selling for $4. XYZ CORP will pay no dividends during the next half year. European put options with the same maturity date and exercise price are selling for $0.67.

Short-sales of stock are strictly illegal. Use a payoff table to show how you can replicate the payoff in 6 months time from short-selling 5 shares today.

(b)Suppose the stock of XYZ CORP is presently selling for $32. Use a payoff table to show how you can make an arbitrage profit. You can buy XYZ's stock.

(c)Now suppose you cannot trade in the stock of XYZ CORP at all, but you can still trade in options. Suppose European put and call options on XYZ CORP stock with a maturity date 6 months hence and an exercise price of $45 are selling for $7 and $1.50 respectively. Also assume that you can trade in the

options in part (a).

Use the put call parity relationship and a payoff table to illustrate an arbitrage strategy which will put money in your pocket today and will have zero payoffs in

all future states of the world.