Pricing equity default swaps under the jump-to-default extended CEV model

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-toDefault Extended Constant Elasticity VarianceModel (JDCEV) of Carr and Linetsky. Mathematically, we obtain an analytical solution to the first passage time problem for the JDCEVdiffusion processwith 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 theprevious periodic premium payment up to the triggering event, and determine arbitrage-free equity default swap rates and compare them with CDS rates. Generally, the EDS rate is strictly greater than the correspondingCDS rate. However, when the triggering barrier is set to be a lowpercentage of the initial stock price and the volatility of the underlying firm’s stock price is moderate, the EDS rates 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. Acknowledgements. The authors would like to thank Javier Sesma for his helpful advice on finding roots of Whittaker functions. This research was supported by the National Science Foundation under grant DMS-0802720. R. Mendoza-Arriaga Information, Risk, & Operations Management Dept. (IROM). McCombs School of Business. The University of Texas at Austin. CBA 5.202, B6500. 1 University Station, Austin, TX 78712, Phone: (512) 471 5824. E-mail: [email protected] V. Linetsky Department of Industrial Engineering and Management Sciences, McCormick School of Engineering and Applied Sciences, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, Phone: (847) 491 2084, Web: http://users.iems.northwestern.edu/∼linetsky. E-mail: [email protected] 2 Rafael Mendoza-Arriaga, Vadim Linetsky