Question: Question 1 [24 points] Consider an economy with two dates (t=0.1) and three states at t=1. The following three assets are traded: Asset A has

Question 1 [24 points] Consider an economy with two dates (t=0.1)

Question 1 [24 points] Consider an economy with two dates (t=0.1) and three states at t=1. The following three assets are traded: Asset A has a payoff of xa=(2,0,0) Asset B has a payoff of x=(1,3,0) Asset C has a payoff of xc=(2.2.4) at t=1. In other words, asset B pays off $1 in state 1, $3 in state 2, and $0 in state 3 at t=1. (a) Suppose the prices of asset A, B and C at t=0 are pa=1.8, PB=3.3 and pc=6.2 respectively. Explain whether there is an arbitrage. [6p] (6) A put option on asset C with exercise price E=3 is traded. What is the price of this option at t=0? [3p] (c) Design a portfolio with payoff (0.0.2) at t=1. What is the price of this portfolio at t=0? [4p] Now consider an (equivalent) economy with three save bonds and four dates (t=0,1,2,3). t=1 Payoff =2 3 Price 0 2 0 0 Bond A Bond B Bond C 1 3 0 4 1.80 3.30 6.20 In other words, e.g. bond B costs $3.20 at t=0 and pays off $1 at t=1, $3 at t=2, and $0 at t=3. (d) (e) What is the definition of a yield curve (or term structure of interests)? [2p] Determine the yield curve in this economy. [6] (f) If there is no arbitrage, the yield curve is always flat. Is this statement true? [3p] Question 1 [24 points] Consider an economy with two dates (t=0.1) and three states at t=1. The following three assets are traded: Asset A has a payoff of xa=(2,0,0) Asset B has a payoff of x=(1,3,0) Asset C has a payoff of xc=(2.2.4) at t=1. In other words, asset B pays off $1 in state 1, $3 in state 2, and $0 in state 3 at t=1. (a) Suppose the prices of asset A, B and C at t=0 are pa=1.8, PB=3.3 and pc=6.2 respectively. Explain whether there is an arbitrage. [6p] (6) A put option on asset C with exercise price E=3 is traded. What is the price of this option at t=0? [3p] (c) Design a portfolio with payoff (0.0.2) at t=1. What is the price of this portfolio at t=0? [4p] Now consider an (equivalent) economy with three save bonds and four dates (t=0,1,2,3). t=1 Payoff =2 3 Price 0 2 0 0 Bond A Bond B Bond C 1 3 0 4 1.80 3.30 6.20 In other words, e.g. bond B costs $3.20 at t=0 and pays off $1 at t=1, $3 at t=2, and $0 at t=3. (d) (e) What is the definition of a yield curve (or term structure of interests)? [2p] Determine the yield curve in this economy. [6] (f) If there is no arbitrage, the yield curve is always flat. Is this statement true? [3p]

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