Extend the debt as it is not deeply out-of-the-money

In this paper, we modify the extendible debts model proposed in Longstaff (1990) to help relieve the moral hazard problem induced in the original model. In Longstaff¡¦s model, extending the maturity of the defaulted debts gives the borrower an incentive to default even if the borrower is insolvent. In this paper, we argue that the debt should not be extended if it is defaulted severely. We have shown that the extendible debt valuation can be obtained by the compound option pricing besides the PDE approach. We also have derived the fair interest rate of the extendible debts in this paper.