(a) A trader has a position consisting of: a long one call with strike price L, short one call with strike price 3L and short one call with strike price 4L. Sketch the pay-off diagram at expiry for the above portfolio, assuming that it costs M to set up the entire position. When will it show a profit? (6 marks) (b) i. Let C(t) and P(t) be the prices of European call and put options at time t, respectively, for an underlying security S(t). The options expire at t=T and have the same strike price, K, and r% denotes the prevailing interest rate. Suppose that the Put-Call parity formula for European options is violated due to mis-pricing in the market and C(t)>P(t)+S(t)Ker(Tt). Show how you would set up an arbitrage to profit from the mis-pricing. (8 marks) ii. Prove that an American call should not be exercised before expiration. (3 marks) iii. Show that P(t)max(Ker(Tt)S(t),0) for both American and European puts. (3 marks) (a) A trader has a position consisting of: a long one call with strike price L, short one call with strike price 3L and short one call with strike price 4L. Sketch the pay-off diagram at expiry for the above portfolio, assuming that it costs M to set up the entire position. When will it show a profit? (6 marks) (b) i. Let C(t) and P(t) be the prices of European call and put options at time t, respectively, for an underlying security S(t). The options expire at t=T and have the same strike price, K, and r% denotes the prevailing interest rate. Suppose that the Put-Call parity formula for European options is violated due to mis-pricing in the market and C(t)>P(t)+S(t)Ker(Tt). Show how you would set up an arbitrage to profit from the mis-pricing. (8 marks) ii. Prove that an American call should not be exercised before expiration. (3 marks) iii. Show that P(t)max(Ker(Tt)S(t),0) for both American and European puts