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

Rafael Mendoza-Arriaga*, Vadim Linetsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)513-540
Number of pages28
JournalFinance and Stochastics
Volume15
Issue number3
DOIs
StatePublished - Sep 1 2011

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

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