Pricing Equity Default Swaps Using Structural Credit Models

Abstract

In early 2004, new equity-credit hybrid derivatives that offered a larger spread than vanilla credit default swaps were developed. At the centre of this development was the equity default swap (EDS), which is the subject of this paper. Structural credit models allow the simultaneous modelling of a firm's credit quality and equity value, making them a natural framework to price equity-credit hybrid derivatives. A closed-form expression for the spread of an equity default swap, which incorporates the legal risk of the derivative, is derived in terms of parameters of a general structural model. A specific structural model, that developed by Leland & Toft, is calibrated by equity data and then used to investigate properties of the EDS spread. It is seen that an equity default swap with a low trigger price can have a substantially greater annual spread than a credit default swap. Also, it is shown that unless the dividend yield is very high, the EDS spread increases as a firm's debt-equity ratio increases, assuming that the firm's asset volatility is constant. However, if there are two reference firms with different debt-equity ratios but the same equity volatility, it is shown that there is a complex relationship between EDS spreads.