Assume all options are European, and that the underlying asset is a non-dividend paying stock, unless otherwise specified. (c) The value of a European put option must satisfy the following restriction: Po 2 Xe-T - So where p, is the current put price, S, is the current price of the underlying stock, X is the exercise price, r > O is the annualised continuously compounded risk-free rate, and T is the time till expiration. Prove by contradiction that the above arbitrage restriction must hold, i.e. show that if the condition does not hold, there is an arbitrage opportunity. (4 marks) (d) It is also known that the value of a European put cannot be greater than the present value of its exercise price, i.e. Po O is the annualised continuously compounded risk-free rate, and T is the time till expiration. Prove by contradiction that the above arbitrage restriction must hold, i.e. show that if the condition does not hold, there is an arbitrage opportunity. (4 marks) (d) It is also known that the value of a European put cannot be greater than the present value of its exercise price, i.e. Po