3 Let t = 0 be the current time. At t = 1, the economy can be one of the following three possible growth rates, H= High Growth, M= Medium Growth, and L=Low Growth. The probability of each state are pH,PM and PL, respectively, and pH + PM + PL = 1. This ecnoomy contains only two assets. The first asset is a stock which pays, TH, TM and TL accordingly in each state. The stock price at time-0 is S(0). The second asset is a bond which pays, YH, M and L according in each state. The bond price at time-0 is B(0). a) Is the above market complete? b) Suppose TH = 4, TM = 3 and TL = 5, S(0) 3 and TL = 5, S(0) = 3.7, YH = 0, YM = 1 and L = 0 and B(0) = 0.25. Are there any risk-free asset in the market? c) Can you price all assets in this economy by using the two assets alone? BM d) Suppose there is another asset, J, which pays BH = 2, 3M = 6 and BL = 2.5, can you find the time-0 price of this asset? e) Suppose there is another asset, K, which pays = 6, M = 3 and aL = 2, can you find the time-0 price of this asset? f) Suppose you know that K(0) = 3.25 and C, which is another asset, pays WH = 4, WM 3 and wL = 10, can you find the time-0 price of C? g) What is the sum of the stochastic discount factors? Do they sum equal to 1? h) Find the risk-free rate of this economy. i) Find the risk-neutral probabilty of this economy. =

3 Let t=0 be the current time. At t=1, the economy can be one of the following three possible growth rates, H= High Growth, M= Medium Growth, and L= Low Growth. The probability of each state are pH,pM and pL, respectively, and pH+pM+pL=1. This ecnoomy contains only two assets. The first asset is a stock which pays, H,M and L accordingly in each state. The stock price at time- 0 is S(0). The second asset is a bond which pays, H,M and L according in each state. The bond price at time- 0 is B(0). a) Is the above market complete? b) Suppose H=4,M=3 and L=5,S(0)=3.7,H=0,M=1 and L=0 and B(0)=0.25. Are there any risk-free asset in the market? c) Can you price all assets in this economy by using the two assets alone? d) Suppose there is another asset, J, which pays H=2,M=6 and L=2.5, can you find the time- 0 price of this asset? e) Suppose there is another asset, K, which pays H=6,M=3 and L=2, can you find the time- 0 price of this asset? f) Suppose you know that K(0)=3.25 and C, which is another asset, pays H=4,M= 3 and L=10, can you find the time- 0 price of C ? g) What is the sum of the stochastic discount factors? Do they sum equal to 1 ? h) Find the risk-free rate of this economy. i) Find the risk-neutral probabilty of this economy