CDS pricing with long memory via fractional Lévy processes

Abstract

In this paper, we consider spread rates of credit default swaps (CDSs) in a long memory fractional Lévy setting, i.e. where interest and hazard rates are driven by processes whose autocovariance functions decrease very slowly over time. Empirically, this property can be found in many variables like interest and hazard rates, but the usually applied Markovian models are unable to reflect this. Using earlier results on conditional distributions of fractional Lévy processes, we carry out an extensive analysis of parameter sensitivities useful for researchers and practitioners alike and derive an analytical pricing formula for CDS contracts. A first empirical application is provided as well.