Endogenizing exogenous default barrier models: The MM algorithm

• Published in: Journal of banking & finance Vol. 36; no. 6; pp. 1639 - 1652
• Main Authors: Forte, Santiago, Lovreta, Lidija
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2012; Elsevier; Elsevier Sequoia S.A
• Subjects: Algorithms; Assets; Barriers; Credit; Credit default swaps; Credit risk; Debt; Enterprises; Expected returns; Hidden parameters; Iterative algorithm; Maximization-Maximization algorithm; Optimization algorithms; Prices; Risk assessment; Risk management; Stock prices; Structural credit risk models; Studies; Time series; Value; G13; Structural credit risk models; G12; Iterative algorithm; Hidden parameters
• ISSN: 0378-4266; 1872-6372
• DOI: 10.1016/j.jbankfin.2012.01.010

► We endogenize exogenous default barrier models. ► The optimal default barrier is derived from actual data on equity prices. ► CDS pricing errors are compared for different default barrier specifications. ► The empirically optimal default barrier generates the lowest CDS pricing errors. In this paper, we propose a Maximization–Maximization (MM) algorithm for the assessment of hidden parameters in structural credit risk models. Step M1 updates the value, volatility, and expected return on the firm’s assets by maximizing the log-likelihood function for the time series of equity prices; Step M2 updates the default barrier by maximizing the equity holders’ participation in the firm’s asset value. The main contribution of the method lies in the M2 step, which allows for ‘endogenizing’ the default barrier in light of actual data on equity prices. Using a large international sample of companies, we demonstrate that theoretical credit spreads based on the MM algorithm offer the lowest CDS pricing errors when compared to other, traditional default barrier specifications: smooth-pasting condition value, maximum likelihood estimate, KMV’s default point, and nominal debt.