Abstract
Equity default swaps (EDS) are hybrid credit-equity products that provide a bridge from credit default swaps (CDS) to equity derivatives with barriers. This paper develops an analytical solution to the EDS pricing problem under the jump-to-default extended constant elasticity of variance model (JDCEV) of Carr and Linetsky. Mathematically, we obtain an analytical solution to the first passage time problem for the JDCEV diffusion process with killing. In particular, we obtain analytical results for the present values of the protection payoff at the triggering event, periodic premium payments up to the triggering event, and the interest accrued from the previous periodic premium payment up to the triggering event, and we determine arbitrage-free equity default swap rates and compare them with CDS rates. Generally, the EDS rate is strictly greater than the corresponding CDS rate. However, when the triggering barrier is set to be a low percentage of the initial stock price and the volatility of the underlying firm’s stock price is moderate, the EDS and CDS rates are quite close. Given the current movement to list CDS contracts on organized derivatives exchanges to alleviate the problems with the counterparty risk and the opacity of over-the-counter CDS trading, we argue that EDS contracts with low triggering barriers may prove to be an interesting alternative to CDS contracts, offering some advantages due to the unambiguity, and transparency of the triggering event based on the observable stock price.
Similar content being viewed by others
References
Abad, J., Sesma, J.: Computation of the regular confluent hypergeometric function. Math. J. 5(4), 74–76 (1995)
Abad, J., Sesma, J.: Successive derivatives of Whittaker functions with respect to the first parameter. Comput. Phys. Commun. 156(1), 13–21 (2003)
Albanese, C., Chen, O.X.: Pricing equity default swaps. Risk 18(6), 83–87 (2005)
Asmussen, S., Madan, D., Pistorius, M.: Pricing equity default swaps under an approximation to the CGMY Lévy model. J. Comput. Finance 11(2), 79–93 (2007)
Atlan, M., Leblanc, B.: Time-changed Bessel processes and credit risk. arXiv:math/0604305v1, April 2006. Working Paper
Atlan, M., Leblanc, B.: Hybrid equity-credit modelling. Risk Mag. 18(8), 61–66 (2005)
Borodin, A., Salminen, P.: Handbook of Brownian Motion: Facts and Formulae, 2nd rev. edn. Probability and Its Applications. Birkhäuser, Basel (2002)
Buchholz, H.: The Confluent Hypergeometric Function with Special Emphasis on Its Applications. Springer, Berlin (1969)
Campi, L., Polbennikov, S., Sbuelz, A.: Systematic equity-based credit risk: A CEV model with jump to default. J. Econ. Dyn. Control 33, 93–108 (2009)
Campi, L., Sbuelz, A.: Closed-form pricing of benchmark equity default swaps under the CEV assumption. Risk Lett. 1(3), 107 (2005)
Carr, P., Linetsky, V.: A jump to default extended CEV model: An application of Bessel processes. Finance Stoch. 10, 303–330 (2006)
Cox, J.C.: Notes on option pricing I: Constant elasticity of variance diffusions. J. Portf. Manag. 23, 15–17 (1975). Reprinted from December 1996
Davydov, D., Linetsky, V.: Pricing and hedging path-dependent options under the CEV process. Manag. Sci. 47, 949–965 (2001)
Davydov, D., Linetsky, V.: Pricing options on scalar diffusions: An eigenfunction expansion approach. Oper. Res. 51, 185–209 (2003)
Gutierrez, C.: CME, Citadel launching CDS exchange. http://www.forbes.com/2008/10/07/cme-citadel-cds-markets-equity-cx_cg_1007markets18.html (2008)
Jobst, N., de Servigny, A.: An empirical analysis of equity default swaps I: Univariate insights. SSRN eLibrary: Working Paper Series, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=681121 (2005)
Jobst, N., de Servigny, A.: An empirical analysis of equity default swaps II: Multivariate insights. SSRN eLibrary: Working Paper Series, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=681145 (2005)
Linetsky, V.: Lookback options and diffusion hitting times: A spectral expansion approach. Finance Stoch. 8, 343–371 (2004)
Linetsky, V.: The spectral decomposition of the option value. Int. J. Theor. Appl. Finance 7, 337–384 (2004)
Picone, D.: Pricing and rating CDOs of equity default swaps with NGARCH-M copulae. Working Paper: Cass Business School—London, http://www.defaultrisk.com/_pdf6j4/Pricing_n_Rating_CDOs_o_Eqt_Dflt_Swps_w_NGARCH-M_Cpl.pdf (May 2005)
Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I.: Integrals Series: More Special Functions. Integrals and Series, vol. III. CRC Press, Boca Raton (1990)
Schroder, M.: Computing the constant elasticity of variance option pricing formula. J. Finance 44, 211–219 (1989)
Slater, L.J.: Confluent Hypergeometric Functions. Cambridge University Press, Cambridge (1960)
Weidner, N.J., Melo, J.D., Williams, P.J.: Equity default swaps and their use in CDO transactions. Cadwalader: The Capital Markets Report (Winter 2005), pp. 5–9
Wolcott, R.: Equity default swaps. Two of a kind? Risk Mag. 17(3), 24–27 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mendoza-Arriaga, R., Linetsky, V. Pricing equity default swaps under the jump-to-default extended CEV model. Finance Stoch 15, 513–540 (2011). https://doi.org/10.1007/s00780-010-0139-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00780-010-0139-3
Keywords
- Default
- Credit default swaps
- Equity default swaps
- Credit spread
- Corporate bonds
- Equity derivatives
- Credit derivatives
- CEV model
- Jump-to-default extended CEV model