Journal of Credit Risk

Time series models for credit default swap premiums

Márton Eifert

  • Introduction to Lévy-driven continuous-time ARMA processes (CARMA)
  • Implementation of a method for the recovery of the driving Lévy process
  • Application to a large set of observed CDS premia time series
  • Estimation of the distribution law yields Normal Inverse Gaussian Lévy increments


We present statistical models for the continuous-time dynamics of credit default swap (CDS) premiums within an intensity-based credit risk modeling framework. Based on historical daily CDS premiums for a large set of different corporate reference entities from several developed countries, we fit continuous-time autoregressive movingaverage processes of an appropriate order driven by a Lévy process. We recover the driving noise process, which only shows a stochastic volatility effect for particular branches. On a distributional level, the increments of the noise process are, as a rule, best modeled by a normal inverse Gaussian distribution.

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