MA370 570 Tutorial 2 Exercise Answers PDF

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MA370/570 – Tutorial 2 Exercise - Fall 2020 1. Consider a single period with terminal price matrix 3 2 100 50 S(1, Ω) = 4100 1105 100 140 Is the payoff/cash flow X attainable when (1) X = [200 100 50]T , (2) X = [100 100 140]T .

2. Determine if the following model is arbitrage-free. If yes, one). 2 1 61 ⇥ ⇤ S(0) = 1 2 10 , S(1, Ω) = 6 41 1

find a state-price vector (just 3 12 0 3 07 7 0 05 0 10

3. Consider the following model:

⇥ ⇤ S(0) = 0.9 1 0.25 0.25 ,

2 1 61 S(1, Ω) = 6 41 1

0 1 0 3

1 0 0 0

3 0 17 7 05 0

Is the model arbitrage-free? If yes, find a unique state-price vector and risk-neutral probabilities....