Computing the survival probability in the Madan–Unal credit risk model: application to the CDS market

References

• Abínzano, I., Seco, L., Escobar, M. and Olivares, P., Single and double Black-Cox: Two approaches for modelling debt restructuring. Econ. Model., 2009, 26(5), 910–917.
   Web of Science ®Google Scholar
• Abramowitz, M. and Stegun, A., Handbook of Mathematical Functions, 1972 (Dover Publications: New York).
   Google Scholar
• Altman, E.I. and Kishore, V.M., Almost everything you wanted to know about recoveries on defaulted bonds. Financ. Anal. J., 1996, 52(6), 57–64.
   Google Scholar
• Amos, D.E., Computation of exponential integrals. ACM T. Math. Software, 1980, 6(3), 365–377.
   Web of Science ®Google Scholar
• Anderson, R.W. and Sundaresan, S., Design and valuation of debt contracts. Rev. Financ. Stud., 1996, 9(1), 37–68.
   Web of Science ®Google Scholar
• Ballestra, L.V. and Pacelli, G., A numerical method to price defaultable bonds based on the Madan and Unal credit risk model. Appl. Math. Finance, 2009, 16(1), 17–36.
   Google Scholar
• Ballestra, L.V. and Pacelli, G., Valuing risky debt: A new model combining structural information with the reduced-form approach. Ins.: Math. Econ., 2014, 55(1), 261–271.
   Web of Science ®Google Scholar
• Bäuerle, N., Risk management in credit risk portfolios with correlated assets. Ins.: Math. Econ., 2002, 30(2), 187–198.
   Web of Science ®Google Scholar
• Bernard, C., Courtois, O.L. and Quittard-Pinon, F., Market value of life insurance contracts under stochastic interest rates and default risk. Ins.: Math. Econ., 2005, 36(3), 499–516.
   Web of Science ®Google Scholar
• Bianchi, M.L., An empirical comparison of alternative credit default swap pricing models. Working Paper No. 882, Banca d’Italia, Rome, Italy, 2012.
   Google Scholar
• Björk, T., Arbitrage Theory in Continuous Time, 2009 (Oxford University Press: New York).
   Google Scholar
• Black, F. and Cox, J.C., Valuing corporate securities: Some effects of bond indenture provisions. J. Finance, 1976, 31(2), 351–367.
   Web of Science ®Google Scholar
• Briys, E. and de Varenne, F., Valuing risky fixed rate debt: An extension. J. Financ. Quant. Anal., 1997, 32(2), 239–248.
   Web of Science ®Google Scholar
• Campbell, J.Y. and Taksler, G.B., Equity volatility and corporate bond yields. J. Finance, 2003, 58(6), 2321–2349.
   Web of Science ®Google Scholar
• Cathcart, L. and El-Jahel, L., Semi-analytical pricing of defaultable bonds in a signaling jump-default model. J. Comput. Financ., 2003, 6(3), 91–108.
   Google Scholar
• Cathcart, L. and El-Jahel, L., Pricing defaultable bonds: A middle-way approach between structural and reduced-form models. Quant. Finance, 2006, 6(3), 243–253.
   Web of Science ®Google Scholar
• Chen, C.-J. and Panjer, H., Unifying discrete structural models and reduced-form models in credit risk using a jump-diffusion process. Ins.: Math. Econ., 2003, 33(2), 357–380.
   Web of Science ®Google Scholar
• Cody, W.J., An overview of software development for special functions. In Lecture Notes in Mathematics, edited by G.A. Watson, Vol. 506 pp. 38–48, 2006 (Springer: Berlin).
   Google Scholar
• Crouhy, M., Galai, D. and Mark, R., A comparative analysis of current credit risk models. J. Bank. Finance, 2000, 24(1), 59–117.
   Web of Science ®Google Scholar
• Das, S.R. and Hanouna, P., Implied recovery. J. Econ. Dyn. Control, 2009, 33(11), 1837–1857.
   Web of Science ®Google Scholar
• Davies, B. and Martin, B., Numerical inversion of the Laplace transform: A survey and comparison of methods. J. Comput. Phys., 1979, 33(1), 1–32.
   Web of Science ®Google Scholar
• Duffee, G.R., Estimating the price of default risk. Rev. Financ. Stud., 1999, 12(1), 197–226.
   Web of Science ®Google Scholar
• Duffie, D. and Lando, D., Term structures of credit spreads with incomplete accounting information. Econometrica, 2001, 69(3), 633–664.
   Web of Science ®Google Scholar
• Duffie, D. and Singleton, K.J., Modeling term structures of defaultable bonds. Rev. Financ. Stud., 1999, 12(4), 687–720.
   Web of Science ®Google Scholar
• Elliott, R.J. and Kopp, P.E., Mathematics of Financial Markets, 2005 (Springer: Berlin).
   Google Scholar
• Feng, R. and Volkmer, H.W., Modeling credit value adjustment with downgrade-triggered termination clause using a ruin theoretic approach. Ins.: Math. Econ., 2012, 51(2), 409–421.
   Web of Science ®Google Scholar
• Fontana, C. and Montes, J.M.A., A unified approach to pricing and risk management of equity and credit risk. J. Comput. Appl. Math., 2014, 259, 350–361.
   Web of Science ®Google Scholar
• Franks, J.R. and Torous, W., An empirical investigation of U.S. firms in reorganization. J. Finance, 1989, 44(3), 747–769.
   Web of Science ®Google Scholar
• Gaver, D.P. Jr, Observing stochastic processes, and approximate transform inversion. Oper. Res., 1966, 14(3), 444–459.
   Web of Science ®Google Scholar
• Giesecke, K., Default and information. J. Econ. Dyn. Control, 2006, 30(11), 2281–2303.
   Web of Science ®Google Scholar
• Grundke, P. and Riedel, K.O., Pricing the risks of default: A note on Madan and Unal. Rev. Deriv. Res., 2004, 7(2), 169–173.
   Google Scholar
• Hao, X., Li, X. and Shimizu, Y., Finite-time survival probability and credit default swaps pricing under geometric Lévy markets. Ins.: Math. Econ., 2013, 53(1), 14–23.
   Web of Science ®Google Scholar
• Hull, J., Options, Futures and Other Derivatives, 2009 (Pearson Prentice Hall: Upper Saddle River, NJ).
   Google Scholar
• Jankowitsch, R., Pullirsch, R. and Veža, T., The delivery option in credit default swaps. J. Bank. Finance, 2008, 32(7), 1269–1285.
   Web of Science ®Google Scholar
• Jones, E.P., Mason, S.P. and Rosenfeld, E., Contingent claims analysis of corporate capital structures: An empirical investigation. J. Finance, 1984, 39(3), 611–625.
   Web of Science ®Google Scholar
• Kalitkin, N.N. and Panin, I.A., On the computation of the exponential integral. Math. Mod. Comput. Simul., 2009, 1(1), 88–90.
   Google Scholar
• Kim, D.H. and Stock, D., The effect of interest rate volatility and equity volatility on corporate bond yield spreads: A comparison of noncallables and callables. J. Corp. Finance, 2014, 26(June), 20–35.
   Web of Science ®Google Scholar
• Koziol, C., Koziol, P. and Schön, T., Do correlated defaults matter for CDS premia? An empirical analysis. Rev. Deriv. Res., 2015, 18(3), 191–224.
   Web of Science ®Google Scholar
• Kuhlman, K.L., Review of inverse Laplace transform algorithms for Laplace-space numerical approaches. Numer. Algorithms, 2013, 63(2), 339–355.
   Web of Science ®Google Scholar
• Kuznetsov, A., On the convergence of the Gaver-Stehfest algorithm. SIAM J. Numer. Anal., 2013, 51(6), 2984–2998.
   Web of Science ®Google Scholar
• Leland, H.E. and Toft, K.B., Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads. J. Finance, 1996, 51(3), 987–1019.
   Web of Science ®Google Scholar
• Longstaff, F.A. and Schwartz, E.S., A simple approach to valuing risky fixed and floating rate debt. J. Finance, 1995, 50(3), 789–819.
   Web of Science ®Google Scholar
• Luciano, E., Calibrating risk-neutral default correlation. J. Risk Finance, 2007, 8(5), 450–464.
   Google Scholar
• Madan, D.B., Modeling and monitoring risk acceptability in markets: The case of the credit default swap market. J. Bank. Finance, 2014, 47, 63–73.
   Web of Science ®Google Scholar
• Madan, D.B. and Schoutens, W., Break on through to the single side. J. Credit Risk, 2008, 4(3), 3–20.
   Google Scholar
• Madan, D.B. and Unal, H., Pricing the risk of default. Rev. Deriv. Res., 1998, 2(2), 121–160.
   Google Scholar
• Madan, D.B. and Unal, H., A two-factor hazard rate model for pricing risky debt and the term structure of credit spreads. J. Financ. Quant. Anal., 2000, 35(1), 43–65.
   Web of Science ®Google Scholar
• Merton, R.C., On the pricing of corporate debt: The risk structure of interest rates. J. Finance, 1974, 29(2), 449–470.
   Web of Science ®Google Scholar
• Olver, F.W.J. and Maximon, L.C., Bessel functions. In NIST Handbook of Mathematical Functions, edited by W.J. Olver, D.W. Lozier, R.F. Boisvert, C.W. Clark, pp. 217–275, 2010 (Cambridge University Press: New York).
   Google Scholar
• Pan, J. and Singleton, K.J., Default and recovery implicit in the term structure of sovereign CDS spreads. J. Finance, 2008, 63(5), 2345–2384.
   Web of Science ®Google Scholar
• Polyanin, A.D. and Zaitsev, V.F., Handbook of Exact Solutions for Ordinary Differential Equations, 2003 (Chapman & Hall/CRC Press: Boca Raton, Florida).
   Google Scholar
• Poularikas, A.D., The Handbook of Formulas and Tables for Signal Processing, 1999 (CRC Press: Boca Raton, FL).
   Google Scholar
• Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T., Numerical Recipes: The Art of Scientific Computing, 2007 (Cambridge University Press: New York).
   Google Scholar
• Schoutens, W. and Cariboni, J., Lévy Processes in Credit Risk, 2009 (Wiley: West Sussex).
   Google Scholar
• Sepp, A., Extended creditgrades model with stochastic volatility and jumps. Wilmott Mag., 2006, (September), 50–62.
   Google Scholar
• Stehfest, H., Algorithm 368: Numerical inversion of Laplace transform. Commun. ACM, 1970, 13(1), 47–49.
   Web of Science ®Google Scholar
• Tang, K.T., Mathematical Methods for Engineers and Scientists 2 -- Vector Analysis, Ordinary Differential Equations and Laplace Transforms, 2007 (Springer: Berlin).
   Google Scholar
• Zhou, C., The term structure of credit spreads with jump risk. J. Bank. Finance, 2001, 25(11), 2015–2040.
   Web of Science ®Google Scholar