Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30174
Simultaneous Term Structure Estimation of Hazard and Loss Given Default with a Statistical Model using Credit Rating and Financial Information

Authors: Tomohiro Ando, Satoshi Yamashita

Abstract:

The objective of this study is to propose a statistical modeling method which enables simultaneous term structure estimation of the risk-free interest rate, hazard and loss given default, incorporating the characteristics of the bond issuing company such as credit rating and financial information. A reduced form model is used for this purpose. Statistical techniques such as spline estimation and Bayesian information criterion are employed for parameter estimation and model selection. An empirical analysis is conducted using the information on the Japanese bond market data. Results of the empirical analysis confirm the usefulness of the proposed method.

Keywords: Empirical Bayes, Hazard term structure, Loss given default.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1083667

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1333

References:


[1] Altman, E. I. and Saunders, A., 2001. An analysis and critique of the BIS proposal on capital adequacy and ratings. Journal of Banking and Finance, 25, 25--46.
[2] Altman, E. I., Bharath, S. T. and Saunders, A., 2002.Credit ratings and the BIS capital adequacy reform agenda. Journal of Banking and Finance, 26, 909--921.
[3] Anderson, N., Breedon, F., Deacon, M., Derry, A. and Murphy, G., 1996. Estimating and interpreting the yield curve. John Wiley and Sons, Chichester.
[4] Brace, A., Gatarek, D. and Musiela, M., 1997.The Market Model of Interest Rate Dynamics. Mathematical Finance, 7, 127--155.
[5] Cox, D. R., 1972.Regression models and life-tables. Journal of the Royal Statistical Society, Series B, 34, 187--220.
[6] Cox, J. C., Ingersoll, J. E. and Ross, S. A., 1985.A Theory of the Term Structure of Interest Rates.Econometrica, 53, 385--407.
[7] de Boor, C., 1978.A practical guide to splines. Springer, Berlin.
[8] Duffie, D., 1996. Dynamic Asset Pricing Theory, Second Edition.Princeton University Press.
[9] Duffie, D., Pan, J. and Singleton, K. J., 2000. Transform Analysis and Asset Pricing for Affine Jump Diffusions. Econometrica, 68, 1343--1376.
[10] Duffie, D. and Singleton, K. J., 1999. Modeling Term Structures of Defaultable Bonds. Review of Financial Studies, 12, 687--720.
[11] Efron, B. and Tibsirani, R. J., 1993. An introduction to bootstrap. Chapman \& Hall. London.
[12] Eilers, P. H. C. and Marx, B. D., 1996. Flexible smoothing with $B$-splines and penalties (with discussion). Statistical Science, 11, 89--121.
[13] Fisher, M. E., Nychka, D. and Zervos, D., 1995. Fitting the term structure of interest rates with smoothing splines. Federal Reserve Bank Finance and Economics Discussion Paper 95-1, January.
[14] Green, P. J. and Silverman, B. W., 1994. Nonparametric regression and generalized linear models.Chapman \& Hall, London.
[15] Hamilton, D. T., Gupton, G. and Berthault, A., 2001.Default and Recovery Rates of Corporate Bond Issuers: 2000. Special Comment. Moody's Investor Service, Global Credit Research.
[16] Heath, D., Jarrow, R. and Morton, A., 1992.Bond Pricing and Term Structure of Interest Rates: A New methodology for Contingent Claims Valuation. Econometrica, 60, 77--105.
[17] Jarrow, R., 2001.Default Parameter Estimation Using Market Prices. Financial Analysts Journal, 57, 75--92.
[18] Jarrow, R. A. and Turnbull, S. M., 1995.Derivatives on Financial Securities subject to Credit Risk. Journal of Finance, 50, 53--85.
[19] Kijima, M. and Muromachi, Y., 2000a.Credit events and the valuation of credit derivatives of basket type. Review of Derivatives Research, 4, 53--77.
[20] Kijima, M. and Muromachi, Y., 2000b.Evaluation of credit risk of a portfolio with stochastic interest rate and default processes. Journal of Risk, 3, 5--36.
[21] Konishi, S., Ando, T. and Imoto, S., 2004.Bayesian information criteria and smoothing parameter selection in radial basis function networks. Biometrika, 91, 27--43.
[22] Konishi, S. and Kitagawa, G., 1996.Generalised information criteria in model selection. Biometrika, 83, 875--890.
[23] Kusuoka, S., 1999.A remark on default risk models. Advances in Mathematical Economics, 1, 69--82.
[24] Lane, W. R., Looney, S. W. and Wansley, J. W., 1986. An application of the Cox proportional hazards model to bank failure. Journal of Banking and Finance, 10, 511--532.
[25] McCulloch, J. H., 1971. Measuring the term structure of interest rates. Journal of Finance, 26, 19--31.
[26] McCulloch, J. H., 1975. The tax-adjusted yield curve. Journal of Finance, 30, 811--830.
[27] Merton, R. C., 1973.Theory of Rational Option Pricing. Bell Journal of Economics and Management Science, 4, 141--183.
[28] Merton, R. C., 1974.On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29, 449--470.
[29] Moody's Investors Service, 2000.Historical Default Rates of Corporate Bond Issuers, 1920-1999. Global Credit Research.
[30] Nelson, C. R. and Siegel, A. F., 1987.Parsimonious modeling of yield curves. Journal of Business, 60, 473--489.
[31] Schaefer, S. M., 1981. Measuring a tax-specific term structure of interest rates in the market for British government securities. The Economic Journal, 91, 415--438.
[32] Schwarz, G., 1978.Estimating the dimension of a model. Annals of Statistics, 6, 461--464.
[33] Steely, J. M., 1991.Estimating the gilt-edged term structure: basis splines and confidence intervals. Journal of Business, Finance and Accounting, 18, 512--529.
[34] Stone, C. J., 1974. Cross-validatory choice and assessment of statistical predictions (with discussion). Journal of the Royal Statistical Society, Series B, 36, 111--147.
[35] Tierney, L. and Kadane, J. B., 1986.Accurate approximations for posterior moments and marginal densities.Journal of the American Statistical Association, 81, 82--86.
[36] Unal, H., Madan, D. and Guntay, L., 2003.Pricing the risk of recovery in default with absolute priority rule violation. Journal of Banking and Finance, 25, 1001--1025.
[37] Vasicek, O. A., 1977. An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5, 177--188.
[38] Vasicek, O. A. and Fong, H. G., 1982. Term structure modeling using exponential splines. Journal of Finance, 37, 339--356.