Optimal Capital Structure, Credit Spreads and Endogenous Default in Stochastic Rates Environment

This paper generalizes the Leland-Toft (1996) structural model of corporate debt by integrating stochastic interest rates through the Longstaff-Schwartz (1994) framework, addressing critical limitations of the original approach. While the Leland-Toft model provides a foundation for analyzing optimal leverage and bond pricing, it exhibits significant practical shortcomings, most notably a systematic overprediction of corporate credit spreads across maturities as identified by Huang. Its assumption of a constant risk-free rate oversimplifies real-world dynamics and contributes to these inaccuracies. Our extension fundamentally enhances the model by incorporating the stochastic nature of interest rates. This modification enables the pricing of floating-rate debt, significantly reduces the model’s overprediction of credit spreads, and corrects errors in the sensitivity to interest rate shocks present in the original framework. Crucially, we demonstrate that the stochastic nature of interest rates is not a marginal factor but plays a vital role: incorporating a non-constant term structure substantially lowers prediction errors, and the correlation between firm asset value and interest rate shocks introduces a mechanism for risk diversification, suggesting firms can increase value by investing in projects inversely related to rate movements. Furthermore, our model generates novel insights, revealing that high-risk corporate bonds can exhibit negative durations under specific conditions, a phenomenon aligning with recent empirical evidence. We rigorously analyze optimal debt structures, establishing that floating and fixed coupon debt are not equivalent. While their values converge for long debt maturities, optimal choice for short maturities depends critically on market expectations: floating debt is preferable if rates are expected to rise, and fixed debt is favored if rates are expected to fall. The model preserves the established empirical link from Leland-Toft, confirming that optimal leverage increases with debt maturity. Sensitivity analysis confirms our framework substantially reduces endogenous default levels compared to Leland-Toft under normal market conditions, directly addressing Huang’s critique regarding spread overprediction. However, the model remains static, leading to non-stationary leverage ratios inconsistent with empirical observations (e.g., Fama), and endogenous default effects on debt structure choice warrant further exploration. Future research should empirically validate the model’s predictive power on real bond data, investigate its ability to resolve the credit spread puzzle, examine the prevalence of mixed fixed/floating debt structures (particularly in contexts like Russia’s inverted yield curve environment), and develop dynamic extensions incorporating optimal control to ensure stationary leverage.