Problems of Existing Estimation Approaches

In this section, we first summarize in Table 1 the existing empirical works of structural models in terms of their subject of research, estimation methods and input data. Next, we briefly summarize the problems of the most popular existing estimation approaches that have been pointed out in the literature^viii.

Problems of Volatility Restriction Approach

Duan (1994) addressed that the shortcoming of the volatility restriction method. The volatility relationship used in volatility restriction method is a redundant condition which provides a restriction only because the equity volatility is inappropriately treated as a constant, which is calculated from historical data. Moreover, since the volatility restriction approach is not statistical, it provides no distribution information about the parameters and cannot perform statistical inferences. In addition, Duan et al. (2003) also pointed out that the drift of the unobservable asset process could not be estimated by the JMR-RV method since the theoretical equity pricing formula does not contain the drift of the asset value process under the physical probability measure. As a result, the default probability could not be obtained.

Ericsson and Reneby (2005) also argued that the described volatility restriction effect implies that increasing stock prices result in underpriced bonds, while decreasing stock prices produce overpriced bonds. Ericsson and Reneby (2005) performed a simulation experiment and compared the performance of the transformed data maximum likelihood estimators with those of the volatility restriction method. Under the settings of four scenarios of different financial risk and business risk levels, they chose to test three structural models including the Black-Scholes-Merton model, the Briys and de Varenne (1997) model, and the Leland and Toft (1996) model. They found that the bias of the transformed-data maximum likelihood approach is negligible for practical purposes in 12 of the Monte Carlo experiments, while the VR approach exhibits an average spread error of 23%.

Problems of the KMV Approach^ix

Duan et al. (2004) prove that the KMV method produces the point estimate identical to the transformed data ML estimate in the context of the Merton (1974) model. However, the KMV method cannot provide the sampling error of the estimate, which is crucial for statistical inference. In short, the KMV method can be regarded as an incomplete ML method.

Moreover, in general, structural models may contain unknown parameters other than the firm’s asset value and volatility: for example, the unknown parameters specific to the financial distress level in the barrier models. In these models, estimates of the KMV method no longer coincide with those of the EM algorithm, and therefore the KMV method cannot generate a meaning estimate for these variables.

Problems of Proxy Approach

Eom, Helwege and Huang (EHH) (2004) use the sum of the market value of equity and total debt as a proxy of the asset value of a firm. That is, V_proxy =K +S. However, Li and Wong (2008) show this assumption is unreasonable even under Merton’s model. Under the option

theory, assuming the true asset value V_true , one can find

) , , ( )

, ,

(V K T S V K C V K T

C _true = = _proxy− < _proxy . The inequality above comes from the fact that

a call option premium must be higher than its intrinsic value before the maturity date. Since

call option is an increasing function of its underlying asset, the relationshipV_true <V_proxyis implied byC(V_true,K,T)<C(V_proxy,K,T). Therefore, we can find that the EHH approach overestimates the true asset value, and it yields biased estimation results. As the market value of assets has been overestimated, the predicted price of corporate bonds will be too high and the corresponding predicted yield spread will be underestimated. This implies the European option framework will automatically be rejected whenever the proxy approach is adopted.

Wong and Choi (2009) further criticize the proxy approach under the down-and-out call option framework of Brockman and Turtle (2003). They show that employing the proxy is equivalent to presuming that the default barrier is greater than the future promised payment of liabilities. This result holds for the arbitrary sets of input parameters including industrial sector, option maturity, and rebate level. Hence, it explains why the hypotheses test and robustness tests of Brockman and Turtle (2003) work well. Firms are presumed to have positive barriers exceeding the book value of corporate liabilities, and no doubt the implied barriers in Brockman and Turtle (2003) are significantly positive.

Table 1 Summary of Previous Empirical Studies of Structural Models

Research Subject Estimation Method Main Input Data for the Estimation Wei and Guo (1997) Credit Spreads Yield Curve Approach Eurodollar and T-Bill Data

Anderson and Sundaresan (2000) Bond Pricing and Yield Spreads Asset Value Proxy Yield Indices of Investment Lyden and Saraniti (2001) Bond Pricing and Yield Spreads Asset Value Proxy Matrix Bond Prices Delianedis and Geske (2001) Bond Pricing and Yield Spreads Volatility Restriction Matrix Bond Prices Huang and Huang (2003) Bond Pricing and Yield Spreads Calibration Bond Prices Eom, Helwege, and Huang (2004) Bond Pricing and Yield Spreads Asset Value Proxy with Refined

Volatility Estimation Bond Prices

Hsu, Saà-Requejo, and Santa-Clara (2003) Bond Pricing GMM Exchange Traded Bond Prices Ericsson and Reneby (2004) Yield Spreads MLE Stock Prices, Bond Prices, Dividend

Information Chen, Fabozzi, Pan, and Sverdlove (2005) CDS Spreads Minimize of Pricing Error and

Absolute Pricing Error CDS Transaction Data

Ericsson, Reneby, and Wang (2006) CDS Premia and Bond Pricing MLE Credit Default Swaps, Bond Prices Vassalou and Xing (2004) Equity Returns KMV (Simplified) Equity Prices

Brockman and Turtle (2003) Default Prediction and Default

Boundary Asset Value Proxy Equity Prices Bharath and Shumway (2008) Default Prediction KMV (Simplified) Equity Prices Chen, Hu, and Pan (2006) Default Prediction Volatility Restriction Equity Prices Wong and Choi (2009) Default Barrier MLE Equity Prices Davydenko (2007) Default Prediction and Default

Boundary

Market values of bond, equity,

and bank loan Bond Prices, Bank loans, Equity Prices Leland (2004) Default Probability Estimation Calibration Moody’s Corporate Bond Default Data