(Sovereign Default Model) Let it be a risk free rate on the T-Bills. Let Dt be...

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(Sovereign Default Model) Let it be a risk free rate on the T-Bills. Let Dt be the amount of debt. When the government issues the amount of debt D, and defaults on it, the household consumption with any given n € (0, 1) in the next period is given by Ct+1 = (1 − n)Yt+1 -0.4D (Default) (4) When the government does not default, the household consumption in the next period is given by Ct+1=Y+1 D₁ (No-Default) (5) Finally, the income shock in the next period Y+1 is uniformly distributed from 0.5 to 1.5. That is, the probability density function for Y₁+1 is given by f(yt+1) = = 1 if 0.5 ≤ Yt+1 ≤ 1.5 f(yt+1) = 0, otherwise (6) (7) The face value of one unit of this bond is 1, and the fact that the government issues Dt amount of debt means that it issues D, units of bonds, so that the government needs to pay back D, to the creditors when it does not default. Finally, the government defaults on its bond when the value of default is strictly larger than that of no-default. a) (10 marks) Let i be a rate of return on the sovereign debt when the government defaults on it. Suppose that the creditors bought this bond for a price of 0.9. Compute i implied from the household consumption for the case of default. b) (20 marks) let it = 0 and n = 0.3. (i) Find a range of D₁ such that even risk-averse investors ask for no risk-premium on the bond. (ii) Find a range of D₁ such that the bond price is zero. (Note that Dt ≥ 0). c) (10 marks) let it = 0 and n = 0.3. Graph a probability of default as a function of Dt (you can use your pen and pencil for this). The x-axis is D and D ≥ 0. d) (10 marks) let i = 0. Let the government issue D₁ = 1. What is the value of n which makes the government default at the probability of 0.5 given D₁ = 1 in the next period?. (Sovereign Default Model) Let it be a risk free rate on the T-Bills. Let Dt be the amount of debt. When the government issues the amount of debt D, and defaults on it, the household consumption with any given n € (0, 1) in the next period is given by Ct+1 = (1 − n)Yt+1 -0.4D (Default) (4) When the government does not default, the household consumption in the next period is given by Ct+1=Y+1 D₁ (No-Default) (5) Finally, the income shock in the next period Y+1 is uniformly distributed from 0.5 to 1.5. That is, the probability density function for Y₁+1 is given by f(yt+1) = = 1 if 0.5 ≤ Yt+1 ≤ 1.5 f(yt+1) = 0, otherwise (6) (7) The face value of one unit of this bond is 1, and the fact that the government issues Dt amount of debt means that it issues D, units of bonds, so that the government needs to pay back D, to the creditors when it does not default. Finally, the government defaults on its bond when the value of default is strictly larger than that of no-default. a) (10 marks) Let i be a rate of return on the sovereign debt when the government defaults on it. Suppose that the creditors bought this bond for a price of 0.9. Compute i implied from the household consumption for the case of default. b) (20 marks) let it = 0 and n = 0.3. (i) Find a range of D₁ such that even risk-averse investors ask for no risk-premium on the bond. (ii) Find a range of D₁ such that the bond price is zero. (Note that Dt ≥ 0). c) (10 marks) let it = 0 and n = 0.3. Graph a probability of default as a function of Dt (you can use your pen and pencil for this). The x-axis is D and D ≥ 0. d) (10 marks) let i = 0. Let the government issue D₁ = 1. What is the value of n which makes the government default at the probability of 0.5 given D₁ = 1 in the next period?.