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2. (20 pts) Let u be the up factor, d be the down factor, and r be the interest rate. Consider the following 4 financial

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2. (20 pts) Let u be the up factor, d be the down factor, and r be the interest rate. Consider the following 4 financial markets. (i) u = 1.1, d=.95, r = 0.05 (ii) u= 1.5, d=1.0, r = 0. (iii) u= = 1.2,d=.9, r = 0.2. (iv) u=2, d= .6, r = 0.3. (a) Which of the market (s) has/have arbitrage. Please specify your reason. (b) Find the risk-neutral probability {, } for the arbitrage-free market(s) in part (a). 2. (20 pts) Let u be the up factor, d be the down factor, and r be the interest rate. Consider the following 4 financial markets. (i) u = 1.1, d=.95, r = 0.05 (ii) u= 1.5, d=1.0, r = 0. (iii) u= = 1.2,d=.9, r = 0.2. (iv) u=2, d= .6, r = 0.3. (a) Which of the market (s) has/have arbitrage. Please specify your reason. (b) Find the risk-neutral probability {, } for the arbitrage-free market(s) in part (a)

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