Assume all options are European, and that the underlying asset is a non-dividend paying stock, unless otherwise specified.

Q1(i) The value of a European put option must satisfy the following restriction: 0 ^(t ) 0 where 0 is the current put price, 0 is the current price of the underlying stock, is the exercise price, > 0 is the annualised continuously compounded risk-free rate, and 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)

(ii) It is also known that the value of a European put cannot be greater than the present value of its exercise price, i.e. 0 ^(t ) 0. This restriction, along with the one in (c), suggests that the price of a European put can fall below its exercise value prior to maturity. When is this situation likely to arise? Give an intuitive explanation as to why its value is below its exercise value in such circumstances.