The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach

This paper considers the dynamics for interest rate processes within a multi-factor Heath, Jarrow and Morton (1992) specification. Despite the flexibility of and the notable advances in theoretical research about the HJM model, the number of empirical studies is still inadequate. This paucity is principally because of the difficulties in estimating models in this class, which are not only high-dimensional, but also nonlinear and involve latent state variables. This paper treats the estimation of a fairly broad class of HJM models as a nonlinear filtering problem, and adopts the local linearization filter of Jimenez and Ozaki (2003), which is known to have some desirable statistical and numerical features, to estimate the model via the maximum likelihood method. The estimator is then applied to the U.S., the U.K. and the Australian markets. Different twoand there-factor models are are found to be the best for each market, with the factors being the level, the slope and the “twist” effect. The contribution of each factor towards overall variability of the interest rates and the financial reward each factor claims are found to differ considerably from one market to another.