Suppose the firm has a single outstanding debt issue with a promised maturity payment of $120 in 5 years. Assume that bankruptcy is triggered by assets (which are observable) falling below $40 in value at any time over the life of the bond—in which case the bondholder receives $40 at that time—or by assets being worth less than $120 at maturity, in which case the bondholder receives the asset value. What is the probability of bankruptcy over the life of the bond? What is the credit spread?
For the first eight problems, assume that a firm has assets of $100, with σ = 40%, α = 15%, and δ = 0. The risk-free rate is 8%.