Convexity Bias in Eurodollar Futures Prices: A Dimension-Free HJM Criterion

Thumbnail Image
Penn collection
Operations, Information and Decisions Papers
Degree type
Heath–Jarrow–Morton model
eurodollar futures
convexity bias
futures rate
forward rate
Other Applied Mathematics
Other Computer Engineering
Theory and Algorithms
Grant number
Copyright date
Related resources
Pozdnyakov, Vladimir
Steele, John M

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.

Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
Journal title
Methodology and Computing in Applied Probability
Volume number
Issue number
Publisher DOI
Journal Issue
Recommended citation