Implied Asset Value Volatility from a New Structural Model of Credit Risk

Abstract

Well-known structural models of credit risk have been shown to underpredict credit spreads, and these models all assume a lognormal firm value diffusion process (FVDP). In this article, I present the formula for pricing corporate liabilities using a normal FVDP that allows negative firm value scenarios that are plausible in real life but are not considered by the lognormal FVDP. And I further show that model-implied asset value volatility from the normal FVDP, unlike those from lognormal structural models, are very close to the empirically estimated asset value volatility for investment-grade companies of different leverage ratios. The same pattern of model-implied asset volatility versus estimates of historical asset volatility is observed from both credit default swap spread and historical default-loss data. Thus, the normal model, by incorporating the economic consideration of negative firm value, is able to explain both observed level of credit spreads and historical default experience with estimates of realized asset value volatility.

TOPICS: Project finance, statistical methods, credit risk management

Key Findings

• • By considering the full range of firm value, the new structural model of credit risk can relate traded credit spreads to empirically estimated asset value volatility.

• • Thus, real-time readings of model-implied asset volatility may be used to quantify the difference between an issuer’s credit quality and its credit spreads.

• • The new model also demonstrates that investment-grade (IG) credit ratings correctly predicting IG companies’ expected default risk, because for IG companies their historical default rate-implied asset value volatility agrees well with estimated historical asset value volatility.