Finance and Stochastics

, Volume 15, Issue 3, pp 513–540

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

Article

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.

Keywords

Default Credit default swaps Equity default swaps Credit spread Corporate bonds Equity derivatives Credit derivatives CEV model Jump-to-default extended CEV model 

Mathematics Subject Classification (2000)

60J35 60J60 60J65 60G70 

JEL Classification

G12 G13 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Information, Risk, & Operations Management Dept. (IROM), McCombs School of BusinessThe University of Texas at AustinAustinUSA
  2. 2.Department of Industrial Engineering and Management Sciences, McCormick School of Engineering and Applied SciencesNorthwestern UniversityEvanstonUSA

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