Call ht the price of a one-period bond that pays 1 in all

Question

Question - Suppose that asset returns satisfy this Euler equation:

1/C_t = E_t0.94(1+r_t+1)1/C_t+1

where r_t+1 denotes the return from period t to period t + 1 and C is real consumption in the US. For simplicity suppose there is no inflation. Suppose that in any period C can take on two values, 1.00 and 1.02, each with probability 0.5. There is no autocorrelation in consumption.

(a) Call h_t the price of a one-period bond that pays 1 in all states of the world in period t + 1. Find the interest rate on this bond first when C_t = 1 and second when C_t = 1.02.

(b) Call h_jt the price of a one-period bond (issued by a sovereign government in an emerging economy) that pays 1 in period t+ 1 with probability 1 - λ and pays 0.8 with probability λ. The event of this partial default is uncorrelated with the value of consumption in period t + 1. Solve for the expected return on this bond first when C_t = 1 and second when C_t = 1.02.

(c) How could an analyst estimate the value of the default probability λ?