Digital Premium

Abstract

Credit default swaps cover two different risks: the event risk of a default and the recovery risk arising from the fact that the recovery percentage is unknown. A digital default swap makes a fixed payment in case of default, and is therefore unaffected by the recovery rate. However, as this article demonstrates, recovery risk does affect digital default swap valuation when calibration is done against market spreads from conventional CDS. This is because uncertainty about the recovery rate in a CDS interacts with the nonlinearity of the price-yield relationship to produce a Jensen's Inequality effect. That is, if the expected value of the recovery rate is used to back out an implied expected default probability from a market CDS spread, the result will understate the true probability of default due to Jensen's Inequality. The market price for a digital default swap therefore includes a kind of premium, in that it will reflect the market's estimate of the true probability of a default event, and possibly a risk premium for the uncertainty around that expectation, rather than the biased probability that would be implied out from the CDS spread.