The term structure of interest rates in a heterogeneous monetary union

BIS Working Papers  |  No 1165  | 
01 February 2024



The prevailing view of the effects of asset purchase programmes revolves around the "duration risk extraction" channel. Under this mechanism, purchases of long-maturity bonds flatten the yield curve by reducing the term premium that private markets demand to compensate for duration risk. The short end of the curve is anchored by the risk-free short rate.

However, the movements of euro area yield curves in response to the pandemic outbreak in early 2020 and to the European Central Bank's subsequent monetary policy response challenge this view. Duration extraction might explain the flattening of the German yield curve after the pandemic emergency purchase programme (PEPP) announcement. However, it offers no explanation for the much larger movements in the Italian and Spanish yield curves. A key feature of these movements is the large shift in the short end of the peripheral curves, which cannot be explained by term premium considerations. The same is true for the large upward shift in peripheral yield curves as the pandemic shock unfolded (before PEPP was announced). This cannot be explained by the pandemic's impact on the amount of duration risk expected to be absorbed by the market.


This paper proposes a model of the term structure of sovereign interest rates designed to address a heterogeneous monetary union like the euro area. We decompose bond yields into four components:

(i)  an expectations term that represents the expected future path of the risk-free rate;

(ii) a term premium representing the risk-averse compensation for bearing duration risk;

(iii) an expected default loss, which captures the compensation that a risk-neutral investor would require for holding defaultable bonds; and

(iv) a credit risk premium that represents the risk-averse compensation for absorbing default risk (over and above expected default losses).

We calibrate our model to Germany and Italy.


Our model distinguishes the "duration extraction channel" from a "default risk extraction channel" that operates through the credit risk premium rather than the term premium: risk-averse investors demand less compensation to hold a defaultable bond when less default risk is outstanding in the market.

We find that default risk extraction is more relevant than duration extraction, driving the response of the Italian yield curve to the PEPP announcement as well as the asymmetry of the responses of the German and Italian curves.

More generally, we find that most of the average sovereign spread in the 1999–2022 period is explained by credit risk premia, ie the risk-averse pricing of default risk, rather than expected default losses, ie the amount of default risk itself.


We build an arbitrage-based model of the yield curves in a heterogeneous monetary union with sovereign default risk, which can account for the asymmetric shifts in euro area yields during the Covid-19 pandemic. We derive an affine term structure solution, and decompose yields into term premium and credit risk components. In an extension, we endogenize the peripheral default probability, showing that it decreases with central bank bond-holdings. Calibrating the model to Germany and Italy, we show that a "default risk extraction" channel is the main driver of Italian yields, and that flexibility makes asset purchases more effective.

JEL classification: E5, G12, F45

Keywords: sovereign default, quantitative easing, yield curve, affine model, Covid-19 crisis, ECB, pandemic emergency purchase programme