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Stw) denotes the share price at time t for a given path w. The share S satisfies the following filtration (P+)7-o, where T = 2 years, the interest rate r = 0 and the prices are in USD. Note that these share prices assume no dividend will be paid at any time. wi S(0) S(ly) S(2y) 4 8 16 4 8 4 4 2 4 4 2 1 W3 W4 Consider the American call option struck at 3 and let D be the unknown dividend amount in USD. (iii) Show that the American call option is greater in value than the European call option by D/3 USD. Give an intuitive reason why this is the case. (iv) Describe what effect a positive USD interest rate will have on the American option value. Stw) denotes the share price at time t for a given path w. The share S satisfies the following filtration (P+)7-o, where T = 2 years, the interest rate r = 0 and the prices are in USD. Note that these share prices assume no dividend will be paid at any time. wi S(0) S(ly) S(2y) 4 8 16 4 8 4 4 2 4 4 2 1 W3 W4 Consider the American call option struck at 3 and let D be the unknown dividend amount in USD. (iii) Show that the American call option is greater in value than the European call option by D/3 USD. Give an intuitive reason why this is the case. (iv) Describe what effect a positive USD interest rate will have on the American option value