(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 Dt and defaults on it, the household consumption with any given ne (0, 1) in the next period is given by
Cₜ₊₁ = (1-n)Yₜ₊₁ (Default)
When the government does not default, the household consumption in the next period is given by
Cₜ₊₁=Yₜ₊₁1 Dt (No- Default)
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 ≤ Ytₜ₊₁ ≤ 1.5 (3) (4)
f(yₜ₊₁) = 0, otherwise
a) An investor bought the bond issued by the government at the price of P. What is the return on this bond when the government defaults (i.e., compute id)?
b) Let i = 0 and n = 0.4, and the investors are risk-neutral. (i) Find a range of Dt such that the bond price for this debt is the same as that for the T-Bills. (ii) Find a range of Dt such that the bond price is zero. (Note that D ≥ 0). (iii) Find a range of D, such that no investors would buy this bond in the government bond auction market.
c) Let it = 0 and n = 0.4, Dt = 0.4, and the investors are risk-neutral. What is the probability of default on this debt, pa ? What is the sovereign spread on this debt when the government issues D = 0.4 amount of debt in the government bond auction market?