This paper empirically tests five structural models of corporate bond pricing: those of Merton (1974), Geske (1977), Leland and Toft (1996), Longsta# and Schwartz (1995), and Collin-Dufresne and Goldstein (2001). We implement the models using a sample of 182 bond prices from firms with simple capital structures during the period 1986-1997. The conventional wisdom is that structural models do not generate spreads as high as those seen in the bond market, and true to expectations we find that the predicted spreads in our implementation of the Merton model are too low. However, most of the other structural models predict spreads that are too high on average. Nevertheless, accuracy is a problem, as the newer models tend to severely overstate the credit risk of firms with high leverage or volatility and yet su#er from a spread underprediction problem with safer bonds. The Leland and Toft model is an exception in that it overpredicts spreads on most bonds, particularly those with high coupons. More accurate structural models must avoid features that increase the credit risk on the riskier bonds while scarcely a#ecting the spreads of the safest bonds.

This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in the shapes of yield curves. We begin by overviewing the dynamic term structure models that have been fit to treasury or swap yield curves and in which the risk factors follow diffusions, jump-diffusion, or have “switching regimes. ” Then the goodness-of-fits of these models are assessed relative to their abilities to: (i) match linear projections of changes in yields onto the slope of the yield curve; (ii) match the persistence of conditional volatilities, and the shapes of term structures of unconditional volatilities, of yields; and (iii) to reliably price caps, swaptions, and other fixed-income derivatives. For the case of defaultable securities we explore the relative fits to historical yield spreads. 1

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Using a set of structural models, we evaluate the price of default protection for a sample of US corporations. Credit default swaps (CDS) are commonly thought to be less influenced by non-default factors, making them an interesting source of data for evaluating models of default risk. In contrast to previous evidence from corporate bond data, CDS premia are not systematically underestimated. In fact, one of our studied models has little difficulty on average in predicting their level. For robustness, we perform the same exercise for bond spreads by the same issuers on the same trading date. As expected, bond spreads are systematically underestimated, consistent with their being driven by significant non-default components. Considering theoretical and market levels alone is insufficient to evaluate the models’ performance, as other factors might be at play in both markets. With this in mind, we relate the models’ residuals by means of linear regressions to default and non-default proxies. We find little evidence of any default risk component in either bond or CDS residuals. However, in the residuals for bonds, we find strong evidence for non-default components, in particular an illiquidity premium. CDS residuals reveal no such

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for their financial backing and for giving me the opportunity to keep a toe in the credit markets. I would like to thank all those at OCIAM who have provided me with the guidance and support necessary to complete this thesis. I am particularly grateful to my supervisor, William Shaw, for allowing me the freedom to pursue my own research interests and I would especially like to thank Christoph Reisinger for more helpful discussions than I can count, not to mention the opportunity to play with his code. I would also like to mention all my friends, in Oxford and elsewhere, who have contributed in so many ways to my life over the last three years and to the ultimate form of my research. Finally, I would like to thank my family for their continued support in all my endeavours, and in particular, my sister, for giving me the impetus I needed to return to student life and Multi-asset credit derivatives trade in huge volumes, yet no models exist that are capable of properly accounting for the spread behaviour of dependent

This paper describes how structural bond pricing models can be estimated using a Simulated Maximum Likelihood procedure developed by Durbin and Koopman (1997). The approach has the advantage that price data on any traded claim (such as bonds, equity, and credit default swaps), as well as information about the balance sheet (e.g. accounting data) can be used in the estimation, improving efficiency. Monte Carlo evidence as well as a small application to real data indicates that this approach is superior to both traditional estimation methods and recently proposed versions of Maximum

Estimating default barriers from market information Brockman and Turtle (2003) develop a barrier option framework to show that default barriers are significantly positive. Most implied barriers are typically larger than the book value of corporate liabilities. We show theoretically and empirically that this result is biased due to the approximation of the market value of corporate assets by the sum of the market value of equity and the book value of liabilities. This approximation leads to a significant overestimation of the default barrier. To get rid of this bias, we propose a maximum likelihood (ML) estimation approach to estimate the asset values, asset volatilities, and default barriers. The proposed framework is applied to empirically examine the default barriers of a large sample of industrial firms. This paper documents that default barriers are positive but not very significant. In our sample, most of the estimated barriers are lower than the book values of corporate liabilities. In addition to the problem with the default barriers, we find significant biases on the estimation of asset value and asset volatility by Brockman and Turtle (2003). JEL classification: G12; G33

This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. We measure bank vulnerability in emerging markets using the distance-to-default, a riskneutral indicator based on Merton’s (1974) structural model of credit risk. The indicator is estimated using equity prices and balance-sheet data for 38 banks in 14 emerging market countries. Results show it can predict a bank's credit deterioration up to nine months in advance. The distance-to-default, hence, may prove useful for bank monitoring purposes.

In this paper it is analyzed whether a Fourier based approach can be an efficient tool for calculating risk measures in the context of a credit portfolio model with integrated market risk factors. For this purpose, this technique is applied to a version of the well-known credit portfolio model CreditMetrics extended by correlated interest rate and credit spread risk. Unfortunately, the characteristic function of the credit portfolio value at the risk horizon can not be calculated in closed-form, but has to be computed by Monte Carlo simulations. Due to this drawback, in the considered numerical examples the performance of the Fourier based approach is not better than that of a full Monte Carlo simulation of the future credit portfolio distribution, especially for inhomogeneous portfolios and when percentiles corresponding to high confidence levels are needed. The application of standard Importance Sampling techniques for improving the performance of the Fourier based approach is problematic, too. Keywords: credit risk, interest rate risk, credit spread risk, credit portfolio model, Value at Risk, characteristic