Default Parameter Estimation Using Market Prices

This article presents a new methodology for estimating recovery rates and the (pseudo) default probabilities implicit in both debt and equity prices. In this methodology, recovery rates and default probabilities are correlated and depend on the state of the macroeconomy. This approach makes two contributions: First, the methodology explicitly incorporates equity prices in the estimation procedure. This inclusion allows the separate identification of recovery rates and default probabilities and the use of an expanded and relevant data set. Equity prices may contain a bubble component—which is essential in light of recent experience with Internet stocks. Second, the methodology explicitly incorporates a liquidity premium in the estimation procedure—which is also essential in light of the large observed variability in the yield spread between risky debt and U.S. Treasury securities and the illiquidities present in risky-debt markets. The available models for pricing credit risk can be divided into two types—structural and reduced form. Structural models endogenize the bankruptcy process by explicitly modeling the asset and liability structure of the company. Reduced-form models exogenously specify an arbitrage-free evolution for the spread between default-free and credit-risky bonds. The two approaches seem to have partitioned the market data: Structural models use only equity prices, and reduced-form models use only debt prices. This partitioning is artificial and unnecessary. One particular parameterization of the structural approach—one of several that have been successfully implemented in professional software—uses only equity prices and balance sheet data to estimate the bankruptcy process parameters. The argument is that debt markets are too illiquid and debt prices too noisy to be useful; hence, they should be ignored. Unfortunately, this implementation of the structural approach ignores the possibility of stock price bubbles (e.g., as we have seen recently for Internet stocks) and the misspecification that such bubbles imply. At the same time, the existing literature on implementing reduced-form models concentrates on debt prices and ignores equity prices. Both markets provide relevant information about a company's default risk and parameters, however, and both should be used. The new methodology for implementing reduced-form models presented here includes both debt and equity prices in the estimation procedure. The methodology takes the approach of estimating recovery rates and the (pseudo) default probabilities implicit in debt and equity prices. The method is quite general; it allows default probabilities and recovery rates to be correlated and to be dependent on the state of the macroeconomy. This flexibility generates a reduced-form model that integrates market and credit risk with correlated defaults. My approach makes two contributions. First, the methodology explicitly incorporates equity prices in the reduced-form estimation procedure, which is unlike current models that use debt prices only. For a fractional recovery rate, the use of debt prices alone allows estimation of only the expected loss—that is, the multiplicative product of the recovery rate times the (pseudo) default probabilities. The introduction of equity prices enables one to separately estimate these quantities. Moreover, the procedure I use to include equity in the reduced-form model is one that is commonly used in portfolio theory literature. Simply stated, the equity price is viewed as the present value of future dividends and a resale value. The future resale value is consistent with the existence of equity price bubbles. In light of the recent market experience with Internet stocks, such an inclusion is necessary for accurate estimation of bankruptcy parameters using equity prices. The second contribution of the method is that it explicitly incorporates liquidity risk in the model and the estimation procedure. Debt markets are notoriously illiquid, especially in comparison with equity markets. Thus, a liquidity-risk adjustment is needed to accurately estimate the bankruptcy parameters from credit spreads. Liquidity risk introduces an important and necessary additional randomness in the yield spread between risky-bond prices and the prices of U.S. Treasury securities. In this methodology, liquidity risk is introduced through the notion of a “convenience yield,” a well-studied concept in the commodities pricing literature that is consistent with an arbitrage-free but incomplete debt market. Adding the randomness allows for the decomposition of the credit spread into a liquidity-risk component and a credit-risk component.