Affine Models, Credit Spreads and the Delivery Option of a Multi-Issuer Bond Future

Abstract

The contribution of this paper is two-fold: Firstly we use the intensity-based framework of Duffie/Singleton (1999) to analyse empirically the credit spread between Italian and German government bonds in an affine model framework. Secondly we value the delivery option of a multi-issuer bond-future contract. This contract allows the short to deliver bonds of different issuers and, therefore, depends on the credit spread between these bonds. The empirical part studies the valuation of German and Italian bonds using two-factor affine models. Similar to Pearson/Sun (1994) we combine cross-sectional and time-series information to estimate the process parameters with maximum likelihood. From our results we conclude that two-factor models produce about the same pricing errors for German and Italian bonds. However, both models explain only imperfectly the observed convex shape and the volatility smile of the default-spread structure. In the second part we analyse the delivery option of a bond future that is similar to the German Bund Future but allows additionally to deliver Italian government bonds. In contrast to our results for the valuation of coupon bonds we find that the option values in both models differ considerably. Our results provide useful insights for empirical work concerning affine intensity based models for the valuation of default-risky bonds and options that depend on a credit spread.