In this scenario, we create an asset backed security (ABS) with four mortgages. These mortgages...
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In this scenario, we create an asset backed security (ABS) with four mortgages. These mortgages either pay off or default, and the probability of a default is 0.3. The defaults are independent across the mortgages. We create four tranches (senior1, senior2, mezzanine, and equity). The senior1 tranche defaults only if all four mortgages default, and the equity tranche defaults if any mortgage defaults.
a) Calculate the probability of default for each of the four tranches.
b) Suppose that each mortgage was worth $1,000,000, such that the total pool is $4,000,000. If the price of a tranche is equal to its expected value, price the senior1 tranche and the equity tranche.
c) Suppose we now form a new security made up of mezzanine tranches. That is, we combine four securities with the same probability of default you calculated for the mezzanine tranche in part a). Call this a CDO. Again, tranche this new security into four parts with the same pattern of seniority. Calculate the probability of default of the various tranches of the CDO.
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