Find a range of dt such that the sovereign spreads

Reference no: EM133319198

Sovereign Default Model Let i∗t be a risk free rate on the T-Bills. Let Dt be the amount of debt. When the government issues the amount of debt Dt and defaults on it, the household consumption with any given η ∈ (0, 1) in the next period is given by

Ct+1 = (1 - η)Yt+1 - 0.4Dt (Def ault) (1) When the government does not default, the household consumption in the next period is given by

Ct+1 = Yt+1 - Dt (No - Default) (2)

Finally, the income shock in the next period Yt+1 is uniformly distributed from 0.5 to 1.5 . That is, the probability density function for Yt+1 is given by

f(yt+1)=1 if 0.5≤yt+1 ≤1.5 (3) f(yt+1) = 0 ,otherwise (4)

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 Dt units of bonds, so that the government needs to pay back Dt to the creditors when it does not default.

Question 1: Let iDt 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 iDt implied from the household consumption for the case of default.

Question 2: let i∗t = 0 and η = 0.3. (i) Find a range of Dt such that the sovereign spreads on this bond are zero. (ii) Find a range of Dt such that the bond price is zero. (Note that Dt ≥ 0).

Question 3: let i∗t = 0 and η = 0.3. (i) Graph a probability of default as a function of Dt (you can use your pen and pencil for this). The x-axis is Dt and Dt ≥ 0. ii) The unit price of a sovereign bond whose face value is one, is computed in the following:

Pb= 1 (1-pd), 1 + i ∗t

where pd denotes the probability of default for the government.. (ii) Graph the bond price as a function of Dt. (iii) The government's revenue for issuing Dt amount of debt is PbDt (note that Pb is a unit price.) Graph the government's revenue as a function of Dt.

Question 4: At which Dt, the government's revenue is maximized? Let D ¯ be the amount of debt which maximizes the government's revenue. Is there any incentive for the government to issue more than D ¯? Argue why this is true or false.

Reference no: EM133319198

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