[1](Put Call Parity with the Present Value ofKnown Dividend D) Let D be the present value of the known dividend(s) on or prior to time T, which is the expiration of a European option.

a)Using non-arbitrage argument, prove

where is the underlying stock price; is the strike price; is the continuously compounded interest rate; is a European call option price; and is a European put option price.

b)Using non-arbitrage argument, prove

where is the underlying stock price; is the strike price; is the continuously compounded interest rate; is an American call option price; and is an American put option price.