We create a CDO with 100 loans of $1 mill each. These loans either pay off or default (Recovery Rate = 0), and the probability of a default of each mortgage is 15%. The defaults are independent across the loans. We create three tranches (senior, mezzanine, and equity). The senior tranche has a principal of $80 mill, the mezzanine tranche has a principal of $15 mill and the equity tranche has a principal of $5 mill. Defaults apply to the equity tranche first, then mezzanine and at last on the senior tranche.

a) Calculate the probability of default (wiped out) for each of the tranches. b) If the price of a tranche is equal to its expected value, calculate the price of each tranche.