A New Functional Setting for Term Structure Modeling Using the Heath–Jarrow–Morton Framework

The well-known Heath–Jarrow–Morton (HJM) framework provides a universal and efficacious instrument for modeling the stochastic evolution of an entire yield curve by explaining the interest rate dynamics in continuous time under no-arbitrage conditions. Existing implementations involve exponentially weighted function spaces as theoretical settings for the former stochastic evolution. While the choice of weight can have a drastic effect on model calibration and subsequent forecasting, it cannot be estimated from market data and does not allow for any objective interpretation. The proposed approach does not have this shortcoming as it adopts a suitably designed unweighted function space. The HJM equation is discretized using a finite difference approach. The resulting semiparametric model is then calibrated on real-world yield data with a new type of functional principal component analysis (PCA)-based approach. Backtesting and benchmarking are conducted against the one-factor Vasicek model using historical data to illustrate its simulation capabilities for prediction and uncertainty quantification. Additionally, in contrast to widely studied US treasuries, negative interest rates are observed for AAA Euro Bonds during the sample period employed for this study. Accordingly, the framework allows for the possibility of negative yields.