The traditional approach has been widely used throughout the empirical corporate bond pricing literature. In this section we discuss these papers and their results.
Rosenfeld (1984) (commonly known as JMR). In their analysis, they consider a dataset of 27 firms with simple capital structures during the period January 1975 to January 1981. The bonds in their set are mostly of investment grade and have sinking fund options. These bonds are also callable since almost all bonds issued during the considered time period are of this type. They use this data to test the effectiveness of the Merton model to price corporate bonds. The model they imple- ment is more a variation of the Merton model since pricing their dataset requires pricing of the call and sinking fund options embedded in the bonds.
In estimating firm value and its volatility, they use a two step procedure. The first step is to form a series of firm values and calculate the volatility as the standard deviation of the returns on these firm values. This method requires the market value of equity and the market value of debt in order to calculate the firm value as the sum of these values. The second step is then to use a ML procedure based on the relationship between equity volatility and firm value volatility as implied by the traditional approach. The second step uses the volatility estimate under the first step. Using this approach requires equity and balance sheet data to estimate firm values. JMR find an average pricing error of 4.52% under the Merton type model. It is difficult, however, to appraise a model’s performance through a pricing error since a small pricing error could still lead to a large spread error. JMR do not report spread errors in their paper.
Ogden (1987) consider a set of 57 bond offerings (and hence 57 prices) of firms with simple capital structures during the period 1973 through to 1985. Like JMR, the set of bonds is callable and has sinking funds, thus Ogden also applies the Merton model considered in JMR. Unlike JMR, Ogden considers the errors in predicted spreads rather than prices in order to test pricing accuracy. Their analysis involves
regressing market spreads on model spreads with the inclusion of a constant. The regression results in a constant of 1.042 and a slope coefficient of 0.925. The pos- itive constant is an indication that the Merton model underpredicts credit spreads (overprices) as is found in the analysis of JMR. In estimating firm value and its volatility, Ogden uses an approach similar to JMR. This method, since using the relation (4.1), is misspecified since equity volatility is estimated as a constant even though the relation used assumes it is stochastic.
Lyden and Saraniti (2000) apply the Merton (1974), and Longstaff and Schwartz (1995) models to data obtained from Bridge Information Systems. Their dataset consists 56 firms with simple capital structures. Their results suggest that both models significantly overprice bonds. That is they underpredict spreads. Lyden and Saraniti estimate firm value volatility through constructing a series of firm val- ues. This is by computing the sum of the market value of equity, book value of liabilities (other than the bond) and the market value of outstanding debt when available. In addition they compute the volatility that sets a model price equal to its corresponding observed price, i.e. a bond-implied volatility.2 This is in order to
check the accuracy of their historical approach. For each volatility estimate, a 95% confidence interval is formed around the estimate. Lyden and Saraniti find that the bond-implied volatility falls outside the confidence interval for 64% of the bonds under the Merton model.
Eom, Helwege and Huang (2004) consider 182 bond prices of firms with simple cap- ital structures during for the last trading day of every December between 1986 and 1997. Their dataset contains senior bonds that contain no embedded options such as call options or sinking funds. They attempt to price these bonds under the Merton
(1974), Geske (1977), Longstaff and Schwartz (1995), Leland and Toft (1996), and Collin-Dufresne and Goldstein (2001) models. As with JMR and Ogden, they find that the Merton model underpredicts spreads observed in the market. Although they observe only a mean pricing error of 1.69% in the Merton model, the mean error in predicted spreads is −50.42% thus showing that the percentage error in price is not sufficient enough to appraise the performance of a model. They also find that the Geske model underpredicts spreads but not as badly as Merton. The mean pricing error for the Geske model is 0.70% with a mean predicted spread error of −29.57% when assuming bondholders receive a constant fraction of the face value when default occurs.3 The results suggest that the Geske model is an improvement
on the Merton model under the PZ approach and that the incorporation of the con- ditional probability of default aids in predicting spreads.
Eom, Helwege and Huang (2004) calculate volatility using historical equity volatil- ity and leverage in a similar manner as JMR and Ogden. They also calculate an alternative measure of asset volatility using bond prices. This method is the same as that of Lyden and Saraniti (2000) where the volatility is chosen as the level that sets the model price under the closed-form solution equal to the actual price. This estimate of volatility results in better pricing accuracy than the above procedure, however, Eom, Helwege and Huang point out that this is not a measure of volatility as such but rather a method that takes pricing errors into account, that is, it is a “catch-all” for errors.4
3Eom, Helwege and Huang also apply the Geske model assuming the bondholders receive the
firm when default occurs. This leads to less variation in predicted spreads, but, does not improve the mean predicted spread error. This is because assuming a constant fraction of face value incorporates the costs of financial distress which increases predicted spreads.
4Eom, Helwege and Huang (2004) do not report the results of using bond-implied volatility in