Staying ahead on the curve: model risk and the term structure

Finance

IFA Working Paper

2000

This paper explores the link between the cross-sectional estimation of the term structure of interest rates and the assumption of absence of dynamic no-arbitrage opportunities. We address questions such as, Are the most commonly used cross-sectional models of the term structure consistent with dynamic no-arbitrage strategies? Or equivalently, can the same cross-sectional model of the term structure be used a) to update the initial condition of the evolution of the yield curve, and b) for the design of dynamic hedging strategies? If this were the case, the same model could be used both for pricing, marking-to-model a book of derivatives, and for risk management reasons. We show that, in general, the answer is negative: in the case of the most generally used cross-sectional models of the term structure, including exponential and cubic splines, any attempt to update the model to newly available information on security prices is necessarily deemed to generate hedging errors that would cumulate over time. The contribution of this paper is to discuss a very simple and parsimonious cross-sectional model of the term structure that is both flexible and consistent with the dynamic no-arbitrage restrictions, so that it can be sensibly used both for marking-to-model purposes and to run risk management strategies. Moreover, this model can be used to construct datasets on implied discount factors and spot rates that do not suffer from spurious violations of the dynamic no-arbitrage restrictions.

Institute of Finance and Accounting

FIN 310

IFA Working Paper

No