Operations, Information and Decisions Papers

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Journal Article

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Methodology and Computing in Applied Probability



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In the theory of interest rate futures, the difference between the futures rate and forward rate is called the “convexity bias,” and there are several widely offered reasons why the convexity bias should be positive. Nevertheless, it is not infrequent that the empirical the bias is observed to be negative. Moreover, in its most general form, the benchmark Heath–Jarrow–Morton (HJM) term structure model is agnostic on the question of the sign of the bias; it allows for models where the convexity bias can be positive or negative. In partial support of the practitioner’s arguments, we develop a simple scalar condition within the HJM framework that suffices to guarantee that the convexity bias is positive. Moreover, when we check this condition on the LIBOR futures data, we find strong empirical support for the new condition. The empirical validity of the sufficient condition and the periodic observation of negative bias, therefore leads one to a paradoxical situation where either (1) there are arbitrage possibilities or (2) a large subclass of HJM models provide interest rate dynamics that fail to capture a fundamental feature of LIBOR futures.

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The final publication is available at Springer via http://dx.doi.org/10.1007/s11009-008-9082-6


Heath–Jarrow–Morton model, eurodollar futures, convexity bias, futures rate, forward rate



Date Posted: 27 November 2017

This document has been peer reviewed.