(6 marks) You are comparing American options to European options. In particular, you are looking into the value added from early exercising. a. (3 marks) Prove using put-call parity that one should never early exercise an American call option on a non-dividend paying stock (explain your steps). b. (2 marks) Use put-call parity to derive an inequality that must be true in order to early exercise an American call option on a dividend paying stock. c. (1 mark) Apply the inequality from b) to the option given below to check whether or not we should early exercise at the given time. An American tall option with the following specifics: The term to maturity is 1 year The underlying pays an annual dividend of $3 at the end of the year The strike price is 50 The current underlying price at time 0.5 is 50 The continuously compounded risk-free interest rate is 4% The price of the option is $3.25 (6 marks) You are comparing American options to European options. In particular, you are looking into the value added from early exercising. a. (3 marks) Prove using put-call parity that one should never early exercise an American call option on a non-dividend paying stock (explain your steps). b. (2 marks) Use put-call parity to derive an inequality that must be true in order to early exercise an American call option on a dividend paying stock. c. (1 mark) Apply the inequality from b) to the option given below to check whether or not we should early exercise at the given time. An American tall option with the following specifics: The term to maturity is 1 year The underlying pays an annual dividend of $3 at the end of the year The strike price is 50 The current underlying price at time 0.5 is 50 The continuously compounded risk-free interest rate is 4% The price of the option is $3.25