Simultaneous Forecasting of Yield Curves for Multiple Zero-Coupon Bonds Using the Heath-Jarrow-Morton Model

Ebenezer Nkum, University of Texas at El Paso


Market diversification is a strategy according to which a company seeks growth by addingproducts and markets that are in a certain sense "uncorrelated" to its existing products andmarkets. Bonds play a major role in a well-balanced diversified portfolio because of theirlow correlation to other asset classes. While the correlations vary widely over time, bondsare not highly correlated with any other asset classes. Even in the simplest diversifiedportfolio, bonds can reduce volatility due to their low or negative correlation with stocks.Because companies can create robust diversified portfolios with bonds it is imperative thatdifferent bonds are studied simultaneously so that portfolios can be created in a coherentmanner. This can facilitate the optimal allocation of investments for multinational and publiccompanies. In fact, many economic studies have revealed that geographical diversification ismore effective in reducing portfolio risk than any of the other investment strategies tested.In this thesis, we present the well-known Heath-Jarrow-Morton (HJM) model which allowsfor the evolution of the entire yield curve by modeling interest rate dynamics in continuoustime under no-arbitrage conditions. We extend the classical HJM model to multi-bond casesin order to study multiple zero-coupon bonds simultaneously. We provide tools to estimatethe correlation structure that may or may not be strongly pronounced. We first assess thethe predictive power of a non-parametric estimation for the HJM model by applying it to theEuro coupon bonds which allow observation of negative interest rate. We also extend thesame scheme to the multi-bond case by applying it to Euro coupon and US coupon bondsand specify the evolution of the short rates by a multivariate Vasicek model. We performstatistical estimation and inference for multi-bond extension of the classical HJM modeland discuss its predictive performance.

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Recommended Citation

Nkum, Ebenezer, "Simultaneous Forecasting of Yield Curves for Multiple Zero-Coupon Bonds Using the Heath-Jarrow-Morton Model" (2021). ETD Collection for University of Texas, El Paso. AAI28714746.