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2. When discussing credit risk in class, we saw that a realization of a low value of a leveraged asset (that is, a property which

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2. When discussing credit risk in class, we saw that a realization of a low value of a leveraged asset (that is, a property which carries a mortgage) could cause the equity owner to minimize his loss by opting to default on his monthly coupon payments, eventually causing the lender(s) to foreclose on his property. One might be hesitant to believe our analysis because we did not explicitly include all of the costs to the equity owner of default, which - in addition to the loss of title to his property - would include a variety of penalties such as either a limited ability to borrow for some number of years after default or obtaining a loan in that period only if he agrees to an exorbitant coupon rate. If we assume these additional costs to default add up to a value (discounted to the time of default) M, we could modify the original graph of the payoffs to the call option we had before. You can use this modification to help you solve the following questions: 4 a. Will the equity owner now refrain from defaulting at a future house value equal or slightly less than the value of his debt, in contrast to his condition for default in the case where there were no additional costs M to the act of defaulting? b. If so, at what value of V1 would he default? c. What is the effect of these additional costs M on the payoff of the risky mortgage to the lender? 2

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