Staying Ahead of the Curve: Model Risk and the Term Structure

This paper explores some issues of model risk in asset pricing, in particular timeinconsistency. Since Ho and Lee (1986), a new class of no-arbitrage models have become increasingly popular both in the asset pricing literature and in the Þnancial industry. These models are said to allow for a perfect Þt of the term structure of the interest rates. In these models the current yield curve is an input so that new observations on the yield curve can be used to update the model at regular frequencies. The primitive securities are always exactly priced. We explore the issue of timeconsistent and self-Þnancing strategies in this class of models.Model risk affects all the three main steps of risk management: speciÞcation, estimation and implementation. Accordingly, we deÞne three concepts of time-inconsistency that deal with these three steps, (a) the joint speciÞcation of the cross-sectional shape of the yield curve and its dynamics, (b) the empirical procedure of estimating the yield curve using observations on bond prices and (c) the implementation and updating of the model. Moreover, we suggest restrictions that need to be satisÞed in order for the risk management procedure to be consistent along these three dimensions. In the empirical part of the paper we assess the economic size of time-inconsistent behaviors in the context of hedging dynamically Þxed income options. We consider both a scenario in which the model is correctly speciÞed but implemented inconsistently and a scenario in which the model is incorrectly speciÞed and the risk manager updates the model using new observations on the yield curve.