Term Structure of CDS Spreads and Risk-Based Capital of the Protection Seller: An Extension of the Dynamic Nelson–Siegel Model with the Business Cycle

Abstract

This article proposes an extended Diebold-Li dynamic Nelson-Siegel model with factors following AR-GARCH processes to fit the term structure of CDS spreads. The proposed model is used to estimate the risk-based capital of a protection seller of CDS contracts. Using CDX North American Investment Grade Index and CDX North American High Yield Index data, we find the AR-GARCH process with the business cycle to outperform all the other models. The risk-based capital for a protection seller increases with the duration of the holding period. Moreover, the protection seller of CDS contracts on high-yield reference entity needs capital-at-risk at least twice the amount that is needed for similar CDS on the investment-grade reference entity. The observed high level of capital-at-risk is driven mainly by the high volatility period identified in our sample, because the low volatility period is characterized by low realized defaults and persistent decline in CDS spreads. TOPICS:Factor-based models, credit default swaps Key Findings • This paper proposes an extended version of the Diebold-Li dynamic Nelson-Siegel (DNS) model to fit the term structure of CDS spreads; with a family of AR-GARCH process with business cycle to capture the dynamics of the conditional mean and the conditional volatility of CDS spreads. • Using data on the CDX North American Investment Grade index (CDXIG) and the CDX North American High Yield index (CDXHY), the proposed model is used to determine the risk-based capital of a protection seller of CDS contracts. • Overall, the proposed AR-GARCH process with the business cycle outperforms all the other processes (AR, AR-GARCH, AR-EGARCH, and AR-GJR), which highlights the importance of the business cycle to better forecast CDS spreads.