[Paper Review] Empirical Evidence for the Structural Recovery Model

Alexander Becker, Alexander F. R. Koivusalo+1 more|arXiv (Cornell University)|Mar 14, 2012

Credit Risk and Financial Regulations4 references3 citations

TL;DR

This paper provides empirical evidence that the structural recovery model derived from the Merton framework accurately describes the inverse relationship between default probability and recovery rate in senior secured bonds, despite the model's simplifying assumptions. Using Moody’s Default and Recovery Database (2000–2010), the study finds strong negative correlation (r = -0.679) and confirms that the Merton-based functional form fits observed data well, with fitted B parameters of 0.882 (2-year maturity) and 0.635 (4-year maturity).

ABSTRACT

While defaults are rare events, losses can be substantial even for credit portfolios with a large number of contracts. Therefore, not only a good evaluation of the probability of default is crucial, but also the severity of losses needs to be estimated. The recovery rate is often modeled independently with regard to the default probability, whereas the Merton model yields a functional dependence of both variables. We use Moody's Default and Recovery Database in order to investigate the relationship of default probability and recovery rate for senior secured bonds. The assumptions in the Merton model do not seem justified by the empirical situation. Yet the empirical dependence of default probability and recovery rate is well described by the functional dependence found in the Merton model.

Motivation & Objective

• To investigate the empirical relationship between default probability and recovery rate in credit portfolios.
• To test whether the functional dependence of recovery rate on default probability derived from the Merton structural model holds in real-world data.
• To assess the validity of the Merton model's assumptions in light of empirical evidence from Moody’s Default and Recovery Database.
• To determine if the structural recovery model can be reliably applied to credit risk models despite its simplifying assumptions.
• To evaluate the robustness of the model across different maturities and bond types (senior secured and unsecured).

Proposed method

• Constructed credit portfolios using senior secured bonds from Moody’s Default and Recovery Database (2000–2010), grouped by credit rating and maturity.
• Defined default probability (PD) and recovery rate (RR) based on the Merton model’s stochastic asset value process with drift μ, volatility σ, and correlation c.
• Applied the analytical solution for expected recovery rate: ⟨RR(PD)⟩ = (1/PD) × exp(−BΦ⁻¹(PD) + ½B²) × Φ(Φ⁻¹(PD) − B), where B = √((1−c)σ²T).
• Divided the PD scale into 30 equal bins and computed the mean recovery rate within each bin, discarding bins with fewer than five observations.
• Fitted the model parameter B using least-squares regression on the portfolio loss function ⟨L(PD)⟩ = PD − exp(−BΦ⁻¹(PD) + ½B²) × Φ(Φ⁻¹(PD) − B).
• Evaluated results for two- and four-year model-maturities, comparing empirical data to analytical curves.

Experimental results

Research questions

• RQ1 Is there a statistically significant negative correlation between default probability and recovery rate in senior secured bonds?
• RQ2 Does the functional relationship between recovery rate and default probability predicted by the Merton structural model hold empirically in real-world credit data?
• RQ3 How well does the Merton-based structural recovery model fit observed recovery rate behavior across different maturities?
• RQ4 Does the model’s performance vary between senior secured and senior unsecured bonds?
• RQ5 Can the structural recovery model be justified empirically despite its simplifying assumptions (e.g., no coupon payments, single debt maturity)?

Key findings

• A strong negative correlation (r = -0.679) exists between default probability and recovery rate for senior secured bonds rated Caa1, Caa2, and Caa3.
• The same inverse relationship is observed for senior unsecured bonds, with a correlation coefficient of -0.639.
• The empirical dependence of recovery rate on default probability is well described by the Merton model’s analytical functional form.
• For two-year model-maturities, the fitted parameter B was 0.882, indicating higher sensitivity of recovery to default risk over shorter horizons.
• For four-year model-maturities, the fitted B parameter decreased to 0.635, suggesting lower sensitivity over longer investment horizons.
• Despite the Merton model’s unrealistic assumptions (e.g., no coupons, single debt maturity), the empirical data strongly support the structural recovery model’s functional form.