A note on the valuation of risky corporate bonds

Simple formulas for the prices of corporate discount and coupon bonds are found using the Longstaff and Schwartz valuation approach for the debt claims of a firm, where default is triggered by a special state variable: the firm's asset-to-debt-ratio. Instead of keeping the total amount of debt constant over time, it is shown that closed form solutions exist under the alternative assumption that the level of leverage is expected to remain constant over time under the risk-neutralized measure. This encourages a more conservative view on the capital structure policy of the firm which might be appropriate in case the firm is neither willing nor able to reduce its expected level of leverage considerably over time.