Simultaneous Term Structure Estimation of Hazard and Loss Given Default with a Statistical Model using Credit Rating and Financial Information
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.
[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.
[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.
@article{"International Journal of Business, Human and Social Sciences:63813", author = "Tomohiro Ando and Satoshi Yamashita", title = "Simultaneous Term Structure Estimation of Hazard and Loss Given Default with a Statistical Model using Credit Rating and Financial Information", 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.", volume = "3", number = "5", pages = "548-11", }
