Problem 13. You have a pool of securities. It has two one-year zero-coupon bonds: bond BBB has Par value $110 000 000 and bond AA has par value $140 000 000. From your experience you know that in case of default the recovery rate for bonds like BBB is 40%, while for bonds similar to bond AA the recovery rate is 65%. You estimate risk- neutral probability of default of each bond to be 3.5% (bonds' defaults are independent). You have structured three tranches: Super-valued tranche (with 65% of total Par value), Very-good Tranche (with 25% of total Par value) and Just-equity Tranche (the rest). Super-Valued Tranche is the senior tranche (it is paid before any other tranche is paid), while Very-good tranche is the next in seniority (it is paid before the Equity tranche is paid). The (continuous) risk-free rate is 2%. Name the structure. Find all possible payoffs. How much is the structure worth initially (assume we can price the structure by given (risk-neutral) probabilities)? What are the values of each tranche?