Maclachlan, Iain C (2007): An empirical study of corporate bond pricing with unobserved capital structure dynamics.
Download (5MB) | Preview
This work empirically examines six structural models of the term structure of credit risk spreads: Merton (1974), Longstaff & Schwartz (1995) (with and without stochastic interest rates), Leland & Toft (1996), Collin-Dufresne & Goldstein (2001), and a constant elasticity of variance model. The conventional approach to testing structural models has involved the use of observable data to proxy the latent capital structure process, which may introduce additional specification error. This study extends Jones, Mason & Rosenfeld (1983) and Eom, Helwege & Huang (2004) by using implicit estimation of key model parameters resulting in an improved level of model fit. Unlike prior studies, the models are fitted from the observed dynamic term structure of firm-specific credit spreads, thereby providing a pure test of model specification. The models are implemented by adapting the method of Duffee (1999) to structural credit models, thereby treating the capital structure process is truly latent, and simultaneously enforcing cross- sectional and time-series model constraints. Quasi-maximum likelihood parameter estimates of the capital structure process are obtained via the extended Kalman filter applied to actual market trade prices on 32 firms and 200 bonds for the period 1994 to 2000. We find that including an allowance for time-variation in the market liquidity premium improves model specification. A simple extension of the Merton (1974) model is found to have the greatest prediction accuracy, although all models performed with similar prediction errors. At between 28.8 to 34.4 percent, the root mean squared error of the credit spread prediction is comparable with reduced-form models. Unlike Eom, Helwege & Huang (2004) we do not find a wide dispersion in model prediction errors, as evidenced by an across model average mean absolute percentage error of 22 percent. However, in support of prior studies we find an overall tendency for slight underprediction, with the mean percentage prediction error of between -6.2 and -8.7 percent. Underprediction is greatest with short remaining bond tenor and low rating. Credit spread prediction errors across all models are non-normal, and fatter tailed than expected, with autocorrelation evident in their time series. More complex models did not outperform the extended Merton (1974) model; in particular stochastic interest-rate and early default accompanied by an exogenous write- down rate appear to add little to model accuracy. However, the inclusion of solvency ratio mean-reversion in the Collin-Dufresne & Goldstein (2001) model results in the most realistic latent solvency dynamics as measured by its implied levels of asset volatility, default boundary level, and mean-reversion rate. The extended Merton (1974) is found to imply asset volatility levels that are too high on average when compared to observed firm equity volatility. We find that the extended Merton (1974) and the Collin-Dufresne & Goldstein (2001) models account for approximately 43 percent of the credit spread on average. For BB rated trades, the explained proportion rises to 55 to 60 percent. For investment grade trades, our results suggest that the amount of the credit spread that is default related is approximately double the previous estimate of Huang & Huang (2003). Finally, we find evidence that the prediction errors are related to market-wide factors exogenous to the models.
|Item Type:||MPRA Paper|
|Original Title:||An empirical study of corporate bond pricing with unobserved capital structure dynamics.|
|Keywords:||Credit risk, bond pricing, Kalman Filter, Merton model, credit spreads, structural credit models|
|Subjects:||G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing; Trading volume; Bond Interest Rates
C - Mathematical and Quantitative Methods > C5 - Econometric Modeling
G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
|Depositing User:||Iain C Maclachlan|
|Date Deposited:||31. Jan 2011 13:54|
|Last Modified:||15. Feb 2013 15:58|
Acharya, V. V., Bharath, S. T. & Srinivasan, A. (2003), Understanding the recovery rates on defaulted securities, Discussion Paper 4098, C.E.P.R.
Acharya, V. V. & Carpenter, J. N. (2002), ‘Corporate bond valuation and hedging with stochastic interest rates and endogenous bankruptcy’, The Review of Financial Studies 15(5), 1355–1383.
Albanese, C. & Chen, O. (2005), ‘Pricing equity default swaps’, Risk 18(6).
Alderson, M. & Betker, B. (1995), ‘Liquidation costs and capital structure’, Journal of Financial Economics 39, 45–69.
Altman, E. (1984), ‘A further empirical investigation of the bankruptcy cost question’, Journal of Finance 39, 1067–1089.
Altman, E. I., Brady, B., Resti, A. & Sironi, A. (2005), ‘The link between default and recovery rates: Theory, empirical evidence, and implications’, The Journal of Business 78, 2203–2228.
Altman, E. I. & Kishore, V. M. (1996), ‘Almost everything you wanted to know about recoveries on defaulted bonds’, Financial Analysts Journal 52, 57–64.
Altman, E. & Pompeii, J. (2003), ‘Market size and investment performance of defaulted bonds and bank loans: 1987-2001’, Economic Notes 32(2), 147–176.
Anderson, R., Sundaresan, S. & Tychon, P. (1996),‘Strategic analysis of contingent claims’, European Economic Review 40, 871–881.
Anderson, R. W. & Sundaresan, S. (1996), ‘Design and valuation of debt contracts’, The Review of Financial Studies 9, 37–68.
Anderson, R. W. & Sundaresan, S. (2000), ‘A comparative study of structural models of corporate bond yields: An exploratory investigation’, Journal of Finance 24, 255– 269.
Andrade, G. & Kaplan, S. N. (1998), ‘How costly is financial (not economic) distress? Evidence from highly leveraged transactions that became stressed.’, Journal of Finance 53(5), 1443–1493.
Babbs, S. & Nowman, K. B. (1999), ‘Kalman filtering of general Vasicek term structure models’, Journal of Financial and Quantitative Analysis 34, 115–130.
Baker, M. & Wurgler, J. (2002), ‘Market timing and capital structure’, Journal of Finance 57(1), 1–32.
Bakshi, G., Madan, D. & Zhang, F. (2001), Understanding the role of recovery in default risk models: Empirical comparisons and implied rates, Working paper, University of Maryland.
Ball, C. & Torous, W. (1996), ‘Unit roots and the estimation of interest rate dynamics’, Journal of Empirical Finance 3, 215–238.
Barone-Adesi, G. & Colwell, D. B. (1999), ‘Valuing and hedging risky debt with constant elasticity of variance effects’, Presented at the Melbourne Seminar Series, The University of Melbourne Department of Accounting and Finance.
Bedendo, M., Cathcart, L. & El-Jahel, L. (1994), The shape of the term structure of credit spreads: An empirical investigation, Working paper, Tanaka Business School, Imperial College London.
Betker, B. (1995), ‘Management’s incentives, equity’s bargaining power, and deviations from absolute priority in Chapter 11 bankruptcies’, Journal of Business 68(2), 161– 183.
Bharath, S. T. & Shumway, T. (2004), Forecasting default with the KMV-Merton model, Working paper, University of Michigan.
Bierens, H., Huang, J. & Kong, W. (2003), An econometric model of credit spreads with rebalancing, ARCH and jump effects, Working Paper FIN-03-012, Stern School of Business.
Black, F. & Cox, J. C. (1976), ‘Valuing corporate securities: Some effects of bond in- denture provisions’, Journal of Finance 31, 351–367.
Black, F. & Scholes, M. (1973), ‘The pricing of options and corporate liabilities’, Journal of Politcal Economy 81, 637–659.
Bowman, K. O. & Shenton, L. R. (1975), ‘Omnibus test contours for departures from normality based on √b1 and b2’, Biometrika 62(2), 243–250.
Briys, E. & de Varenne, F. (1997), ‘Valuing risky fixed rate debt: An extension’, Journal of Financial and Quantitative Analysis pp. 239–248.
Brown, S. J. & Dybvig, P. H. (1986), ‘The empirical implications of the Cox, Ingersoll, Ross theory of the term structure of interest rates’, Journal of Finance 41, 183–193.
Bruche, M. (2005), Estimating structural bond pricing models via simulated maximum likelihood, Working paper, Financial Markets Group London School of Economics.
Campbell, J. Y. & Taksler, G. B. (2002), Equity volatility and corporate bond yields, Working Paper 8961, National Bureau of Economic Research, Inc.
Campi, L., Polbennikov, S. & Sbuelz, A. (2005), Assessing credit with equity: A CEV model with jump to default, Working Paper 2005-27, Tilburg University.
Campi, L. & Sbuelz, A. (2005), Closed-form pricing of benchmark equity default swaps under the CEV assumption, Working Paper 2005-28, Tilburg University.
Chakravarty, S. & Sarkar, A. (1999), Liquidity in fixed income markets: A comparison of the bid-ask spread in corporate, government, and municipal bond markets, Technical report, Federal Reserve Bank of New York.
Chang, X., Dasgupta, S. & Hilary, G. (2006), ‘Analyst coverage and financing decisions’, The Journal of Finance 61(6), 3009–3048.
Chen, R. & Scott, L. (1995), Multifactor Cox-Ingersoll-Ross models of the term structure: Estimates and tests from a Kalman filter model, Working paper, University of Georgia.
Claessens, S. & Pennacchi, G. (1996), ‘Estimating the likelihood of Mexican default from the market price of Brady bonds’, Journal of Financial and Quantitative Analysis 31, 109–126.
Collin-Dufresne, P. & Goldstein, R. S. (2001), ‘Do credit spreads reflect stationary lever- age ratios?’, Journal of Finance 56, 1929–1957.
Collin-Dufresne, P., Goldstein, R. S. & Helwege, J. (2003), Is credit event risk priced? Modeling contagion via the updating of beliefs, Working paper, Carnegie Mellon University.
Collin-Dufresne, P., Goldstein, R. S. & Martin, J. S. (2001), ‘The determinants of credit spread changes’, Journal of Finance 56(6), 2177–2207.
Cooper, I. & Davydenko, S. (2004), Using yield spreads to estimate expected returns on debt and equity, Working paper, London Business School.
Cox, J. (1975), Notes on option pricing I: Constant elasticity of diffusions. Standford University.
Crosbie, P. J. & Bohn, J. R. (2002), Modeling default risk, Technical report, KMV Corporation.
Crouhy, M., Galai, D. & Mark, R. (2000), ‘A comparative analysis of current credit risk models’, Journal of Banking and Finance 24, 59–117.
Cumby, R. & Evans, M. (1995), The term structure of credit risk: Estimates and specification tests, Working Paper S-95-21, NBER.
Dangl, T. & Zechner, J. (2004), ‘Credit risk and dynamic capital structure choice’, Journal of Financial Intermediation 13, 183–204.
Das, S. & Hanouna, P. (2006), Implied recovery, Working paper, Santa Clara University.
Davydenko, S. (2005), When do firms default? A study of the default boundary, Working paper, London Business School.
Davydenko, S. A. & Strebulaev, I. A. (2004), Strategic actions and credit spreads: An empirical investigation, Working paper, London Business School.
De-Jong, F. (2000), ‘Time series and cross-section information in affine term-structure models’, Journal of Business & Economic Statistics 18(3), 300–314.
Delianedis, G. & Geske, R. (1998), Credit risk and risk neutral default probabilities: Information about rating migrations and defaults, Working paper, The Anderson School at UCLA.
Delianedis, G. & Geske, R. (2001), The components of corporate credit spreads: De- fault, tax, jumps, liquidity, and market factors, Working paper, UCLA Anderson Graduate School of Management.
Demchuk, A. & Gibson, R. (2006), ‘Stock market performance and the term structure of credit spreads’, Journal of Financial and Quantitative Analysis 41(4), 863-887.
Dissanaike, G., Lambrecht, B. & Saragga, A. (2001), ‘Differentiating debt target from non-target firms: An empirical study on corporate capital structure’, Working Paper .
Doornick, J. A. (2002), Object-Orientated Matrix Programming Using Ox, 3rd edn, Timberlake Consultants Press and Oxford, London. http://www.doornick.com.
Duan, J.-C. (2004), ‘Maximum likelihood estimation using price data of the derivative contract’, Mathematical Finance 4(2), 155–167.
Duan, J.-C. & Simonato, J.-G. (1999), ‘Estimating and testing exponential-affine term structure models by Kalman filter’, Review of Quantitative Finance and Accounting 13, 111–135.
Duffee, G. (1998), ‘The relation between treasury yields and corporate bond yield spreads’, Journal of Finance 53(6), 2225–2241.
Duffee, G. (1999), ‘Estimating the price of default risk’, The Review of Financial Studies 12, 197–226.
Duffie, D. & Kan, R. (1996), ‘A yield-factor model of interest rates’, Mathematical Finance 6, 379–406.
Duffie, D., Pederson, L. H. & Singleton, K. J. (2000), Modeling sovereign yield spreads: A case study of Russian debt, Working paper, Graduate School of Business, Stanford University.
Duffie, D., Saita, L. & Wang, K. (n.d.), ‘Multi-period corporate default prediction with stochastic covariates’, Journal of Financial Economics 83, 653–665.
Duffie, D. & Singleton, K. J. (1999), ‘Modeling term structures of defaultable bonds’, The Review of Financial Studies 12, 687–720.
Duffie, D. & Singleton, K. J. (2003), Credit Risk: Pricing, Measurement, and Management, Princeton University Press, Princeton Series in Finance, New Jersey, USA.
Durbin, J. & Koopman, S. J. (2001), Time Series Analysis by State Space Methods, Oxford University Press, Oxford, UK.
Eberhart, A., Moore, W. & Roenfeldt, R. (1990), ‘Security pricing and deviations from the absolute priority rule in bankruptcy proceedings’, Journal of Finance 45(5), 1457–1469.
Eberhart, A. & Sweeney, R. (1992), ‘Does the bond market predict bankruptcy settlements?’, Journal of Finance 47(3), 943–980.
Elton, E. J., Gruber, M. J., Agrawal, D. & Mann, C. (2001), ‘Explaining the rate spread on corporate bonds?’, Journal of Finance 56, 247–277.
Eom, Y. H., Helwege, J. & Huang, J.-Z. (2004), ‘Structural models of corporate bond pricing: An empirical analysis’, The Review of Financial Studies 17(2), 499–544.
Ericsson, J. & Reneby, J. (2002), The valuation of corporate liabilities: Theory and tests, Working paper, McGill University.
Ericsson, J., Reneby, J. & Wang, H. (2003), The valuation of corporate liabilities: Theory and tests, Working paper, SSE/EFI Working Paper Series in Economics and Finance No. 445.
Ericsson, J., Reneby, J. & Wang, H. (2005), Can structural models price default risk? Evidence from bond and credit derivative markets, Working paper, EFA 2005 Moscow Meetings.
Estrella, A. & Mishkin, F. (1998), ‘U.S. recessions: Financial variables as leading indicators’, The Review of Economics and Statistics 80(1), 45–61.
Fama, E. & French, K. (2002), ‘Testing trade-off and pecking order predictions about dividends and debt’, The Review of Financial Studies 15(1), 1–33.
Fan, H. & Sundaresan, S. (2000), ‘Debt valuation, renegotiation, and optimal dividend policy’, The Review of Financial Studies 13(4), 1057–1099.
Ferry, J. (2003), ‘Barra joins crowded market for Merton models’, Risk 16(11).
Fischer, E. O., Heinkel, R. & Zechner, J. (1989), ‘Dynamic capital structure choice: Theory and tests’, Journal of Finance 44(1), 19–40.
Francois, P. & Morellec, E. (2004), ‘Capital structure and asset prices: Some effects of bankruptcy procedures’, Journal of Business 77(2), 387–411.
Frank, M. Z. & Goyal, V. K. (2003), ‘Testing the pecking order theory of capital structure’, Journal of Financial Economics 67, 217–248.
Franks, J. R. & Torous, W. N. (1989), ‘An empirical investigation of U.S. firms in reorganisation’, Journal of Finance 44, 747–769.
Frye, J. (2000), ‘Depressing recoveries’, Risk 13(11), 106–111.
Galai, D., Raviv, A. & Wiener, Z. (2005), Liquidation triggers and the valuation of equity and debt, Working paper, The Hebrew University Business School and Marshall School of Business, University of Southern California.
Geske, R. (1977), ‘The valuation of corporate liabilities as compound options’, Journal of Financial and Quantitative Analysis 12, 542–552.
Geyer, A. & Pichler, S. (1999), ‘A state-space approach to estimate and test multifactor Cox-Ingersoll-Ross models of the term structure’, Journal of Financial Research 22, 107–130.
Gilson, S. (1997), ‘Transaction costs and capital structure choice: Evidence from financially distressed firms’, Journal of Finance 52, 161–196.
Goldstein, R., Ju, N. & Leland, H. (2001), ‘An EBIT-based model of dynamic capital structure’, Journal of Business pp. 483–507.
Gordy, M. B. (2002), A risk-factor model foundation for ratings-based bank capital rules, Working Paper 2002-55, The Federal Reserve Board.
Graham, J. & Harvey, C. (2001), ‘The theory and practice of corporate finance: Evidence from the field’, Journal of Financial Economics 60, 187–243.
Guedes, J. & Opler, T. (1996), ‘The determinants of the maturity of corporate debt issues’, Journal of Finance 51(1), 1809–1833.
Guha, R. (2003), Recovery of face value at default: Empirical evidence and implications for credit risk pricing, Working paper, London Business School.
Hamilton, J. D. (1994), Time Series Analysis, Princeton University Press, Princeton, New Jersey, USA.
Harrison, J. M. (1985), Brownian Motion and Stochastic Flow Systems, John Wiley and Sons, New York.
Harvey, A. C. (1989), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press, Cambridge, UK.
Helwege, J. & Turner, C. M. (1999), ‘The slope of the credit yield curve for speculative- grade issuers’, Journal of Finance 54(5), 1869–1884.
Hong, G. & Warga, A. (2000), ‘An empirical study of bond market transactions’, Financial Analysts Journal March/April, 32–46.
Hovakimian, A., Opler, T. & Titman, S. (2001), ‘The debt-equity choice’, Journal of Financial and Quantitative Analysis 36(1), 1–24.
Hsu, J., Saa-Requejo, J. & Santa-Clara, P. (2003), Bond pricing with default risk, Working Paper 1245, The Anderson Graduate School of Management at UCLA.
Huang, J. & Huang, M. (2003), How much of the corporate-treasury yield spread is due to credit risk? A new calibration approach, Working paper, Pennsylvania State University.
Hull, J., Nelken, I. & White, A. (2004), Merton’s model, credit risk, and volatility skews, Working paper, University of Toronto.
BIBLIOGRAPHY 259 Jalilvand, A. & Harris, R. (1984), ‘Corporate behaviour in adjusting to capital structure and dividend targets: An econometric study’, Journal of Finance 39, 127–145.
James, J. & Webber, N. (2001), Interest Rate Modelling, John Wiley & Sons Ltd, Chichester, UK.
Jarrow, Lando, T. (1997), ‘A Markov model for the term structure of credit risk spreads’, The Review of Financial Studies 10, 481–523.
Jarrow, R. A. & Turnbull, S. M. (1995), ‘Pricing derivatives on financial securities subject to credit risk’, Journal of Finance 50, 53–86.
Jensen, M. C. (1986), ‘Agency costs of free-cash-flow, corporate finance and takeovers’, American Economic Review 76(2), 323–329.
Jensen, M. C. & Meckling, W. H. (1976), ‘Theory of the firm: Managerial behavior, agency costs and ownership structure’, Journal of Financial Economics 3, 305– 360.
Jones, P., Mason, S. & Rosenfeld, E. (1983), ‘Contingent claims analysis of corporate capital structures: An empirical investigation’, Journal of Finance 39, 611–625.
Kayhan, A. & Titman, S. (2007), ‘Firms’ histories and their capital structures’, Journal of Financial Economics 83(1), 1–32.
Keswani, A. (2005), Estimating a risky term structure of Brady bonds, Working Paper 73, The Manchester School.
Kim, J., Ramaswamy, K. & Sundaresan, S. (1993), ‘Does default risk in coupons affect the valuation of corporate bonds? A contingent claims model’, Financial Management pp. 117–131.
Korajczyk, R. & Levy, A. (2003), ‘Capital structure choice: Macroeconomic conditions and financial constraints’, Journal of Financial Economics 68, 75–109.
Leland, H. (1994), ‘Corporate debt value, bond covenants, and optimal capital structure’, Journal of Finance 49, 1213–1252.
Leland, H. (1998), ‘Agency costs, risk management and capital structure’, Journal of Finance pp. 1213–1243.
Leland, H. (2004), ‘Predictions of expected default frequencies in structural models of debt’, Journal of Investment Management 2(2), 1–16.
Leland, H. E. & Toft, K. B. (1996), ‘Optimal capital structure, endogenous bankruptcy and the term structure of credit spreads’, Journal of Finance 51, 987–1019.
Lemmon, M. & Zender, J. (2002), Debt capacity and tests of capital structure theories, Working paper, David Eccles School of Business, University of Utah.
Litterman, R. & Iben, T. (1991), ‘Corporate bond valuation and the term structure of credit spreads’, Journal of Portfolio Management pp. 52–64.
Longstaff, F. A. (2002), The flight-to-liquidity premium in U.S. Treasury bond prices, Working paper, The Anderson School at UCLA.
Longstaff, F. A., Mithal, S. & Neis, E. (2005), ‘Corporate yield spreads: Default risk or liquidity? New evidence from the credit default swap market’, Journal of Finance 60(5), 2213–2253.
Longstaff, F. A. & Schwartz, E. S. (1995), ‘A simple approach to valuing risky fixed and floating rate debt’, Journal of Finance 50(3), 789–819.
Lund, J. (1997), Econometric analysis of continuous-time arbitrage-free models of the term structure of interest rates, Working paper, The Aarhus School of Business.
Lyden, S. & Saraniti, D. (2000), An empirical examination of the classical theory of corporate security valuation, Technical report, Bourne Lyden Capital Partners and Barclays Global Investors.
Madan, D. B. & Unal, H. (1999), A two-factor hazard-rate model for pricing risky debt and the term structure of credit spreads, Working paper, The Wharton School of Business, University of Pennsylvania.
Madan, D. & Unal, H. (1996), Pricing the risks of default, Working Paper 94-16-B, University of Maryland.
Marsh, P. (1982), ‘The choice between equity and debt: An empirical study’, Journal of Finance pp. 121–144.
Medova, E. A. & Smith, R. G. (2004), Pricing equity default swaps using structural credit models, Working Paper WP 12/2004, The Judge Institute of Management, University of Cambridge.
Mella-Barral, P. & Perraudin, W. (1997), ‘Strategic debt service’, Journal of Finance 52, 531–556.
Merton, R. (1974), ‘On the pricing of corporate debt: The risk structure of interest rates’, Journal of Finance 29, 449–470.
Merton, R. (1976), ‘Option pricing when underlying stock returns are discontinuous’, Journal of Financial Economics 3, 125–144.
Modigliani, F. & Miller, M. (1958), ‘The cost of capital, corporation finance, and the theory of investment’, American Economic Review 48, 655–669.
Moraux, F. (2002), Valuing corporate liabilities when the default threshold is not an absorbing barrier, Working paper, Universite ́ de Rennes I.
Mueller, C. (2000), A simple multi-factor model of corporate bond prices, Doctoral dissertation, University of Wisconsin-Madison.
Myers, S. (1977), ‘Determinants of corporate borrowing’, Journal of Financial Economics 5, 147–175.
Myers, S. C. (1984), ‘The capital structure puzzle’, Journal of Finance 39, 575–592.
Myers, S. C. & Majluf, N. S. (1984), ‘Corporate financing and investment decisions when firms have information the investors do not have’, Journal of Financial Economics 13, 187–221.
Nandi, S. (1998), ‘Valuation models for default-risky securities: An overview’, Federal Reserve Bank of Atlanta Economic Review pp. 22–35.
Nelson, C. R. & Siegel, A. F. (1985), ‘Parsimonious modeling of yield curves’, Journal of Business 60, 473–489.
Nielsen, L. T., Saa-Requejo, J. & Santa-Clara, P. (1993), Default risk and interest rate risk: The term structure of default risk, Working paper, INSEAD.
Ogden, J. (1987), ‘Determinants of the ratings and yields on corporate bonds: Tests of the contingent claims model’, The Journal of Financial Research 10, 329–339.
Opler, T. C. & Titman, S. (1994), ‘Financial distress and corporate performance’, Journal of Finance 49, 1015–1040.
Pennacchi, G. (1991), ‘Identifying the dynamics of real interest rates and inflation: Evidence using survey data’, The Review of Financial Studies 4, 53–86.
Reinhart, V. & Sack, B. (2002), ‘The changing information content of market interest rates’, BIS Quarterly Review pp. 40–50.
Roberts, M. (2002), The dynamics of capital structure: An empirical analysis of a partially observable system, Working paper, University of California at Berkeley.
Saa-Requejo, J. & Santa-Clara, P. (1999), Default risk and interest rate risk: The term structure of default risk, Working paper, The Anderson Graduate School of Management at UCLA.
Sarig, O. & Warga, A. (1989), ‘Some empirical estimates of the risk structure of interest rates’, Journal of Finance 44(5), 1351–1360.
Schonbucher, P. (2003), Credit Derivatives Pricing Models: Models, Pricing and Implementation, John Wiley & Sons.
Shyam-Sunder, L. & Myers, S. C. (1999), ‘Testing static tradeoff against pecking order models of capital structure’, Journal of Financial Economics 51, 219–244.
Smith, C. W. & Warner, J. B. (1979), ‘On financial contracting: An analysis of bond covenants’, Journal of Financial Economics pp. 117–161.
Sobehart, J. & Stein, R. (2000), Moody’s public firm risk model: A hybrid approach to modeling short term default risk, Technical report, Moody’s Investors Services.
Suo, W. & Wang, W. (2006), Assessing default probabilities from structural credit models, Working paper, Queen’s University, Queen’s School of Business.
Taggart, R. (1977), ‘A model of financial decisions’, Journal of Finance 44, 1467–1484.
Tauren, M. (1999), A model of corporate bond prices with dynamic capital structure, Working paper, Indiana University.
Truck, S., Harpaintner, S. & Rachev, S. T. (2005), A note on forecasting aggregate recovery rates with macroeconomic variables, Working Paper 03/2005, Universitat Karlsruhe.
Tudela, M. & Young, G. (2003), A Merton-model approach to assessing the default risk of UK public companies, Working Paper 194, Bank of England.
Uhrig-Homburg, M. (2002), ‘Valuation of defaultable claims: A survey’, Schmalenbach Business Review 54, 24 – 57.
Varma, P. & Cantor, R. (2004), ‘Determinants of recovery rates on defaulted bonds and loans for North American corporate issuers: 1983-2003’, Special Comment.
Vasicek, O. (1977), ‘An equilibrium characterisation of the term structure’, Journal of Financial Economics 5, 177–188.
Vassalou, M. & Xing, Y. (2004), ‘Default risk in equity returns’, Journal of Finance 59(2), 831–868.
Warga, A. D. (2000), National Association of Insurance Commissioners database, Working paper, University of Houston, Texas.
Warga, A. & Welch, I. (1993), ‘Bondholder losses in leveraged buyouts’, Review of Financial Studies 6(4), 959–982.
Warner, J. (1977), ‘Bankruptcy costs: Some evidence’, Journal of Finance 33, 337–347.
Wei, D. G. & Guo, D. (1997), ‘Pricing risky debt: An empirical comparison of the Longstaff and Schwartz and Merton models’, Journal of Fixed Income 7, 8–28.
Weiss, L. (1990), ‘Direct costs and violation of priority of claims’, Journal of Financial Economics 27, 285–314.
Welch, I. (2004), ‘Capital structure and stock returns’, Journal of Political Economy 112, 106–131.
White, H. (1980), ‘A heteroskedastic-consistent covariance matrix estimator and a direct test for heteroskedasticity’, Econometrica 48, 817–838.
Zhou, C. (1997), A jump-diffusion approach to modeling credit risk and valuing defaultable securities, Working paper, Federal Reserve Board, Washington DC.