The value of the ‘swap’ feature in equity default swaps

Abstract

When equity default swap (EDS) contracts were first included in a rated collateralized debt obligation (CDO) deal, some critics doubted the originality of the product. In fact, EDSs are equivalent to already existing binary barrier options on equity, except the premium is not paid upfront, but over time, and conditional on the trigger event not having occurred. Therefore, as opposed to existing options, the buyer of an EDS: (1) postpones payment for protection, and (2) purchases not only protection against a sharp drop in the price of equity, but also the right to cease payments in case the barrier is hit. This paper derives the closed-form pricing formula for equity default swap spreads under the Black–Scholes assumptions, and then quantifies the fraction of the EDS spread actually due to the ‘swap’ feature of the contract for plausible parameter values. It is found that the extra spread due to the swap nature of EDSs is economically significant only for high volatility, high trigger levels, and long time-to-maturity. The impact of interest rates on the value of the ‘swap’ feature is almost exclusively due to the postponement of payments.

Acknowledgments

The author would like to thank the Editors and an anonymous Referee for helpful comments. Funding from Dirección General de Enseñanza Superior e Investigación Científica, grant SEJ2004-0168/ECON, and Comunidad Autónoma de Madrid, grant 06/HSE/0150/2004, is also gratefully acknowledged.

Notes

†Albanese and Chen (2005) also model the stock price dynamics directly as a pure diffusion process. Because they assume a constant elasticity of variance processs, rather than a geometric Brownian motion, their pricing formula must be implemented numerically. They find that this formula fits the empirically observed EDS to CDS spread ratios more closely than a credit barrier model which incorporates credit jumps and jumps to default. They conclude that jumps do not appear to be priced in the EDS market.

‡See Merton (1973) for an extension of Black and Scholes (1973) to the case of options on dividend paying stock with constant continuously compounded dividend yield.