1. Suppose that an underyling asset S is given by for t e [0, 1] S(t) 3+ te!-! for t e [1,2] 5 - 43 = For the discretely measured case the sampling data are taken at t = mdt where m = 0, .., 4 and dt = 0.5. Consider European options with T = 2. (a) Calculate the continuously sampled arithmetic average for S(t), te [0,2). (b) Calculate the discretely sampled arithmetic average for S(t), t [0,2]. (c) Calculate the discretely sampled geometric average for S(t), te [0, 2]. (d) What is the payoff at expiry of a continuous arithmetic average strike call? (e) What is the payoff at expiry of a discrete geometric average strike put? (f) What is the payoff at expiry of a discrete arithmetic average rate put with E = 4.8