Consider a three-period economy (t = 0,1,2), in which one stock and one riskless bond are...

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Consider a three-period economy (t = 0,1,2), in which one stock and one riskless bond are traded. Assume that the stock follows the process St+1StHt, - where H, can take the values u or d=1,u> 1, with both outcomes being equally likely. Assume that the bond follows the process Bt+1 = B₁R. Let Bo-1 and So be the initial bond price and stock prices respectively. 1. (5 points) Draw an event tree representing the possible outcomes of the stock and bond. price at each period in the economy. 2. (10 points) What are the state prices in this economy? State the conditions for u, R such that there is no arbitrage in this economy. What are the state price densities? Give the Equivalent Martingale Measure for this economy. 3. (10 points) Consider an investor in this economy with utility over consumption. His utility is given by U (C₁, C₂) = Ep log(e₁) + 8 log(e₂)] Given that the investor's initial wealth is Wo, find the optimal consumption choice (ci, e). Consider a three-period economy (t = 0,1,2), in which one stock and one riskless bond are traded. Assume that the stock follows the process St+1StHt, - where H, can take the values u or d=1,u> 1, with both outcomes being equally likely. Assume that the bond follows the process Bt+1 = B₁R. Let Bo-1 and So be the initial bond price and stock prices respectively. 1. (5 points) Draw an event tree representing the possible outcomes of the stock and bond. price at each period in the economy. 2. (10 points) What are the state prices in this economy? State the conditions for u, R such that there is no arbitrage in this economy. What are the state price densities? Give the Equivalent Martingale Measure for this economy. 3. (10 points) Consider an investor in this economy with utility over consumption. His utility is given by U (C₁, C₂) = Ep log(e₁) + 8 log(e₂)] Given that the investor's initial wealth is Wo, find the optimal consumption choice (ci, e).

Answer rating: 100% (QA)

1 The event tree is Period 0 S0 B01 Period 1 uS0 RB0 dS0 R... View the full answer