The Impact of Margin Interest on the Valuation of Credit Default Swaps

Abstract

Virtually all credit default swaps (CDS) are collateralized with a daily cash settlement of the variation margin equal to the change in their mark-to-market values. We show how the interest on the variation margin (also called price alignment interest) affects the value of CDS. Specifically, we show that all CDS can be valued as the expected net present value of the premium and default contingent payments by using the same risk-neutral probability measure but different discounting rates determined by the margin interest rate (i.e., the interest rate used to compute price alignment interest) on the individual CDS. For example, if the margin interest rate is fed funds, then the discounting should be done on the overnight indexed swap (OIS) curve, and if there is no margin interest, then there should be no discounting. We show that arbitrage opportunities can occur if this valuation approach is not used. Finally, using observed market prices, we numerically demonstrate meaningful differences in CDS mark-to-mark values when the OIS curve is used for discounting instead of the customary LIBOR curve.