Consider a Brady bond issued by Mexico with 5 years left to maturity, paying a coupon of 10%. Only the par value is collateralized by American Treasury bonds. Assume that the U.S. spot rate is 5% for all maturities. The face value is $100 and the price of the bond is 93.
a. Calculate the present value of the collateral.
b. Write down the equation that determines the (stripped) yield-to-maturity of the bond.
c. Write down the equation that estimates Mexican government’s default probability p every period.