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, the authors 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 processes with the 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.