A revised version of the Cathcart & El-Jahel model and its application to CDS market. (English) Zbl 1483.91241
The authors are concerned with the pricing of credit default swaps. In previous research, a hybrid model of L. Cathcart and L. El-Jahel [Quant. Finance 6, No. 3, 243–253 (2006; Zbl 1136.91474)] has been proposed. In this paper, the intensity of the default follows from a Vašíček model rather than the CIR interest rate model. This allows for the inclusion of negative interest rates. Also, this approach permits for more efficient use of computer time for calculating prices. This credit model should be of interest to academics and practitioners alike.
Reviewer: John O’Hara (Colchester)
Citations:
Zbl 1136.91474References:
| [1] | Altman, EI; Kishore, VM, Almost everything you wanted to know about recoveries on defaulted bonds, Financ. Anal. J., 52, 6, 57-64 (1996) · doi:10.2469/faj.v52.n6.2040 |
| [2] | Ballestra, L.V., Pacelli, G., Radi, D.: A note on Fergusson and Platen, “Application of maximum likelihood estimation to stochastic short rate models”. Annals of Financial Economics 11(4), 1650,018 (2016) · Zbl 1400.60104 |
| [3] | Ballestra, LV; Pacelli, G.; Radi, D., Computing the survival probability in the Madan-Unal credit risk model: Application to the CDS market, Quant. Finance, 17, 2, 299-313 (2017) · Zbl 1402.91838 · doi:10.1080/14697688.2016.1189590 |
| [4] | Ballestra, LV; Pacelli, G.; Radi, D., Modeling CDS spreads: a comparison of some hybrid approaches, J. Empir. Financ., 57, 107-124 (2020) · doi:10.1016/j.jempfin.2020.03.001 |
| [5] | Bischi, G., Lamantia, F., Radi, D.: Qualitative Theory of Dynamical Systems, Tools and Applications for Economic Modelling, Springer Proceedings in Complexity, chap Qualitative Methods in Continuous and Discrete Dynamical Systems, pp. 1-159. (2016). doi:10.1007/978-3-319-33276-5_1 · Zbl 1372.37005 |
| [6] | Black, F.; Cox, JC, Valuing corporate securities: some effects of bond indenture provisions, J. Financ., 31, 2, 351-367 (1976) · doi:10.1111/j.1540-6261.1976.tb01891.x |
| [7] | Brigo, D.; Mercurio, F., Interest Rate Models-Theory and Practice: With Smile, Inflation and Credit (2007), Berlin: Springer, Springer Finance, Berlin |
| [8] | Cathcart, L.; El-Jahel, L., Semi-analytical pricing of defaultable bonds in a signaling jump-default model, J. Comput. Finance, 6, 3, 91-108 (2003) · doi:10.21314/JCF.2003.105 |
| [9] | Cathcart, L.; El-Jahel, L., Pricing defaultable bonds: a middle-way approach between structural and reduced-form models, Quant. Finance, 6, 3, 243-253 (2006) · Zbl 1136.91474 · doi:10.1080/14697680600670754 |
| [10] | Cox, J.; Ingersoll, JE Jr; Ross, S., A theory of the term structure of interest rates, Econ. J. Econ. Soc., 53, 2, 385-408 (1985) · Zbl 1274.91447 |
| [11] | Das, SR; Sundaram, RK, An integrated model for hybrid securities, Manage. Sci., 53, 9, 1439-1451 (2007) · Zbl 1232.91687 · doi:10.1287/mnsc.1070.0702 |
| [12] | Della Corte, P., Sarno, L., Schmeling, M., Wagner, C.: Exchange rates and sovereign risk. 2354935 (2018) |
| [13] | Duffee, GR, Estimating the price of default risk, Rev. Financ. Stud., 12, 1, 197-226 (1999) · doi:10.1093/rfs/12.1.197 |
| [14] | Duffie, D.; Lando, D., Term structures of credit spreads with incomplete accounting information, Econ. J. Econo. Soc., 69, 3, 633-664 (2001) · Zbl 1019.91022 |
| [15] | Duffie, D.; Singleton, KJ, Modeling term structures of defaultable bonds, Rev. Financ. Stud., 12, 4, 687-720 (1999) · doi:10.1093/rfs/12.4.687 |
| [16] | Feng, R.; Volkmer, HW, Modeling credit value adjustment with downgrade-triggered termination clause using a ruin theoretic approach, Insur. Math. Econ., 51, 2, 409-421 (2012) · Zbl 1284.91561 · doi:10.1016/j.insmatheco.2012.06.007 |
| [17] | Fergusson, K.; Platen, E., Application of maximum likelihood estimation to stochastic short rate models, Ann. Financ. Econ., 10, 2, 1550009 (2015) · doi:10.1142/S2010495215500098 |
| [18] | Fontana, C.; Montes, JMA, A unified approach to pricing and risk management of equity and credit risk, J. Comput. Appl. Math., 259, 350-361 (2014) · Zbl 1314.91227 · doi:10.1016/j.cam.2013.04.047 |
| [19] | Franks, JR; Torous, WN, An empirical investigation of US firms in reorganization, J. Finance, 44, 3, 747-769 (1989) · doi:10.1111/j.1540-6261.1989.tb04389.x |
| [20] | Friedman, A., Stochastic Differential Equations and Applications (1975), New York: Academic Press, New York · Zbl 0323.60056 |
| [21] | Giesecke, K., Default and information, J. Econ. Dyn. Control, 30, 11, 2281-2303 (2006) · Zbl 1162.91458 · doi:10.1016/j.jedc.2005.07.003 |
| [22] | Gross, C.; Siklos, PL, Analyzing credit risk transmission to the nonfinancial sector in europe: A network approach, J. Appl. Economet., 35, 1, 61-81 (2020) · doi:10.1002/jae.2726 |
| [23] | Gündüz, Y.; Uhrig-Homburg, M., Does modeling framework matter? A comparative study of structural and reduced-form models, Rev. Deriv. Res., 17, 1, 39-78 (2014) · Zbl 1285.91139 · doi:10.1007/s11147-013-9090-8 |
| [24] | Guo, X.; Jarrow, RA; Lin, H., Distressed debt prices and recovery rate estimation, Rev. Deriv. Res., 11, 3, 171-204 (2008) · Zbl 1165.91370 · doi:10.1007/s11147-009-9029-2 |
| [25] | Hao, X.; Li, X.; Shimizu, Y., Finite-time survival probability and credit default swaps pricing under geometric Lévy markets, Insurance Math. Econ., 53, 1, 14-23 (2013) · Zbl 1284.91562 · doi:10.1016/j.insmatheco.2013.04.003 |
| [26] | Jankowitsch, R.; Pullirsch, R.; Veža, T., The delivery option in credit default swaps, J. Bank. Finance, 32, 7, 1269-1285 (2008) · doi:10.1016/j.jbankfin.2007.10.012 |
| [27] | Jarrow, RA; Turnbull, SM, Pricing derivatives on financial securities subject to credit risk, J. Financ., 50, 1, 53-85 (1995) · doi:10.1111/j.1540-6261.1995.tb05167.x |
| [28] | Jones, EP; Mason, SP; Rosenfeld, E., Contingent claims analysis of corporate capital structures: An empirical investigation, J. Financ., 39, 3, 611-625 (1984) · doi:10.1111/j.1540-6261.1984.tb03649.x |
| [29] | Krylov, N., Controlled Diffusion Processes (1980), New York: Springer, New York · Zbl 0459.93002 · doi:10.1007/978-1-4612-6051-6 |
| [30] | Lando, D., On Cox processes and credit risky securities, Rev. Deriv. Res., 2, 2-3, 99-120 (1998) · Zbl 1274.91459 |
| [31] | Longstaff, FA; Schwartz, ES, A simple approach to valuing risky fixed and floating rate debt, J. Financ., 50, 3, 789-819 (1995) · doi:10.1111/j.1540-6261.1995.tb04037.x |
| [32] | Madan, DB, Modeling and monitoring risk acceptability in markets: The case of the credit default swap market, J. Bank. Finance, 47, 63-73 (2014) · doi:10.1016/j.jbankfin.2014.05.024 |
| [33] | Madan, DB; Schoutens, W., Break on through to the single side, J. Credit Risk, 4, 3, 3-20 (2008) · doi:10.21314/JCR.2008.076 |
| [34] | Madan, DB; Unal, H., Pricing the risks of default, Rev. Deriv. Res., 2, 2-3, 121-160 (1998) · Zbl 1274.91426 |
| [35] | Madan, DB; Unal, H., A two-factor hazard rate model for pricing risky debt and the term structure of credit spreads, J. Financ. Quant. Anal., 35, 1, 43-65 (2000) · doi:10.2307/2676238 |
| [36] | Merton, RC, On the pricing of corporate debt: The risk structure of interest rates, J. Financ., 29, 2, 449-470 (1974) |
| [37] | Morris, C., Neal, R., Rolph, D.: Credit spreads and interest rates: a cointegration approach. Research Working Paper 98-08, Federal Reserve Bank of Kansas City (1998) |
| [38] | Packer, F., Zhu, H.: Contractual terms and CDS pricing. (2005). BIS Quarterly Review Available at SSRN: https://ssrn.com/abstract=1884901 |
| [39] | Polyanin, A.D., Zaitsev, V.F.: Exact Solutions for Ordinary Differential Equations. Chapman & Hall/CRC (2003) · Zbl 1015.34001 |
| [40] | Schoutens, W.; Cariboni, J., Lévy Processes in Credit Risk (2009), New York: Wiley, New York · Zbl 1192.91008 |
| [41] | Shreve, SE, Stochastic Calculus for Finance II: Continuous-Time Models (2010), Springer Finance: Springer, Springer Finance |
| [42] | Teschl, G., Ordinary Differential Equations and Dynamical Systems, Graduate Studies in Mathematics (2012), New York: American Mathematical Society, New York · Zbl 1263.34002 · doi:10.1090/gsm/140 |
| [43] | Vasicek, O., An equilibirum characterization of the term structure, J. Financ. Econ., 5, 2, 177-188 (1977) · Zbl 1372.91113 · doi:10.1016/0304-405X(77)90016-2 |
| [44] | Zhou, C., The term structure of credit spreads with jump risk, J. Bank. Finance, 25, 11, 2015-2040 (2001) · doi:10.1016/S0378-4266(00)00168-0 |
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