Empirical analysis and calibration of the CEV process for pricing equity default swaps

Equity Default Swaps (EDSs) are credit-like instruments that were first introduced in 2003. EDSs are deep out of the money digital put options that pay out a fixed amount (recovery rate) upon the stock price hitting a pre-set low barrier. The premium is paid out as contingent quarterly payments similar to Credit Default Swaps (CDSs). EDSs initially soared in volume as investors used them in capital structure arbitrage strategies involving the simultaneous buying and selling of EDS contracts, as spreads on EDSs were several multiples of CDS spreads. However, the contracts diminished in volume as CDS contracts took over. With the recent financial turmoil in the credit derivatives market, some attention has turned from CDSs and their associated structured correlation products such as Nth-to-default basket and synthetic Collateralized Debt Obligations (CDOs) as CDS markets tend to be opaque and difficult to price. In addition, default correlations are not directly observable and recoveries are stochastic, making pricing and modelling difficult. As against this, the underlying stock prices in EDS are directly observable and the correlation is also directly observable. The EDS may therefore return to the credit fold and may be a complement to the CDS market. In this paper, we examine the pricing of CDSs using the CEV process and calibrate the CEV process to actual observed market prices for EDS; we then draw conclusions on the CEV process, the relationship between stock prices and volatility, and the relationship between CDS and EDS prices.