Are standard structural models able to explain credit spreads on corporate bonds? In contrast to much of the literature, we find that the Black-Cox model matches the level of investment-grade spreads well. Model spreads for speculative-grade debt are too low, and we find that bond illiquidity contributes to this underpricing. Our analysis makes use of a new approach for calibrating the model to historical default rates that leads to more precise estimates of investment-grade default probabilities. Received October 25, 2016; editorial decision January 12, 2018 by Editor Andrew Karolyi. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Stephen M. Schaefer, Eduardo S. Schwartz, A Two-Factor Model of the Term Structure: An Approximate Analytical Solution, The Journal of Financial and Quantitative Analysis, Vol. 19, No. 4 (Dec., 1984), pp. 413-424

ABSTRACT In this paper, we develop a model for valuing debt options that takes into account the changing characteristics of the underlying bond by assuming that the standard deviation of return is proportional to the bond's duration. The resulting model uses the bond price as the single state variable and thus preserves much of the simplicity and robustness of the Black‐Scholes approach. The paper provides comparisons between option prices computed using this model and those using the Black‐Scholes and Brennan and Schwartz models.

In this paper, we develop a model for valuing debt options that takes into account the changing characteristics of the underlying bond by assuming that the standard deviation of return is proportional to the bond's duration. The resulting model uses the bond price as the single state variable and thus preserves much of the simplicity and robustness of the Black-Scholes approach. The paper provides comparisons between option prices computed using this model and those using the Black-Scholes and Brennan and Schwartz models.

This paper attempts to estimate both the direct and indirect costs of regulation for major sectors of the UK financial services industry. We also compare UK direct costs with those for the US and France and this provides a benchmark for assessing the effect of regulation on the competitive position of the UK financial services industry. We believe that this is the first attempt to compare regulatory costs in the UK with those of its major competitors. For indirect costs, in the absence of an international benchmark we compare our results with the predictions made at the time of the introduction of the Financial Services Act, by Lomax (Lomax, D., 1987. London Markets After the Financial Services Act, Butterworths, London) and Goodhart (Goodhart, C., 1988. The costs of regulation. In: Seldon, A. (Ed.), Financial Regulation or Over-regulation. Institute of Economic Affairs, London, p. 31). They estimated that indirect costs would be £4 for every £1 of direct costs and that annual aggregate costs would be £100 million. Our results suggest that, so far as direct costs are concerned, the costs of regulation for the securities and derivatives trading and broking sector are substantially lower for the UK than for the US and France. In contrast, for the investment management and unit trust industry UK costs are significantly higher than those for the other two countries. For the life insurance industry, UK costs are similar to those in France but markedly lower than those for the US. We also find for the securities industry around £4.1 of indirect costs per £1 of direct costs. For the investment management industry the corresponding figure is £3.2. However there is substantial variation across firms and, although our sample is too small to be definitive, the ratio appears to be related to firm size. Although these results are broadly in line with the predictions of Lomax and Goodhart it should be borne in mind that both numerator and denominator are substantially higher in real terms than those used by Lomax and Goodhart.

We study corporate bond default rates using an extensive new data set spanning the 1866–2008 period. We find that the corporate bond market has repeatedly suffered clustered default events much worse than those experienced during the Great Depression. For example, during the railroad crisis of 1873–1875, total defaults amounted to 36% of the par value of the entire corporate bond market. Using a regime-switching model, we examine the extent to which default rates can be forecast by financial and macroeconomic variables. We find that stock returns, stock return volatility, and changes in GDP are strong predictors of default rates. Surprisingly, however, credit spreads are not. Over the long term, credit spreads are roughly twice as large as default losses, resulting in an average credit risk premium of about 80 basis points. We also find that credit spreads do not adjust in response to realized default rates.

Using an extensive data set on corporate bond defaults in the US from 1866 to 2010, we study the macroeconomic effects of bond market crises and contrast them with those resulting from banking crises. During the past 150 years, the US has experienced many severe corporate default crises in which 20–50% of all corporate bonds defaulted. Although the total par amount of corporate bonds has at times rivaled the amount of bank loans outstanding, we find that corporate default crises have far fewer real effects than do banking crises. These results provide empirical support for current theories that emphasize the unique role that banks and the credit and collateral channels play in amplifying macroeconomic shocks.