Abstract
Galluccio and Roncoroni (2006) empirically demonstrate that cross-sectional data provide relevant information when assessing dynamic risk in fixed income markets. We put forward a theoretical framework supporting that finding based on the notion of “shape factors”. We devise an econometric procedure to identify shape factors, propose a dynamic model for the yield curve, develop a corresponding arbitrage pricing theory, derive interest rate pricing formulae, and study the analytical properties exhibited by a finite factor restriction of rate dynamics that is cross-sectionally consistent with a family of exponentially weighed polynomials. We also conduct an empirical analysis of cross-sectional risk affecting US swap, Euro bond, and oil markets. Results support the conclusion whereby shape factors outperform the classical yield (resp., price) factors ( i.e., level, slope, and convexity) in explaining the underlying fixed income (resp., commodity) market risk. The methodology can in principle be used for understanding the intertemporal dynamics of any cross-sectional data.
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