Deriving implied risk-free interest rates from bond and CDS quotes: a model-independent approach

Abstract

We propose a market-consistent approach to the definition and construction of the implied term structure of the risk-free interest rates which are model-independent with respect to the choice of the fitting method. The main idea consists of the simultaneous fitting of the credit default swap (CDS) and the defaultable bond quotes where the theoretical prices are calculated in the framework of the reduced-form modelling of credit risk under standard assumptions. We obtain not only the implied risk-free zero-coupon yield curve but also the implied issuer-specific hazard rate curves. Prior to fitting, we perform a selection of bond issues and issuers. Next, we check for data consistency via arbitrage-like reasoning. Typically, the initial data needs a consistency adjustment, namely ‘artificial’ widening of the observed bid-ask spreads for the selected financial instruments. We construct feasibility bands representing achievable precision of the fitting procedure depending on maturity. Then we apply this methodology to determine the term structure of the risk-free rates for the euro zone. This generic approach for the calculation of the risk-free reference rates in the euro zone can be helpful for the purposes of insurers and pension funds. In particular, the relevant term structure can be used in the assessment of technical provisions as requested in Article 77 of the Solvency II Level 1 text.