Date of Award

2021-08-01

Degree Name

Master of Science

Department

Mathematical Sciences

Advisor(s)

Michael M. Pokojovy

Abstract

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 and markets. Bonds play a major role in a well-balanced diversified portfolio because of their low correlation to other asset classes. While the correlations vary widely over time, bonds are not highly correlated with any other asset classes. Even in the simplest diversified portfolio, 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 that different bonds are studied simultaneously so that portfolios can be created in a coherent manner. This can facilitate the optimal allocation of investments for multinational and public companies. In fact, many economic studies have revealed that geographical diversification is more 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 allows for the evolution of the entire yield curve by modeling interest rate dynamics in continuous time under no-arbitrage conditions. We extend the classical HJM model to multi-bond cases in order to study multiple zero-coupon bonds simultaneously. We provide tools to estimate the correlation structure that may or may not be strongly pronounced. We first assess the the predictive power of a non-parametric estimation for the HJM model by applying it to the Euro coupon bonds which allow observation of negative interest rate. We also extend the same scheme to the multi-bond case by applying it to Euro coupon and US coupon bonds and specify the evolution of the short rates by a multivariate Vasicek model. We perform statistical estimation and inference for multi-bond extension of the classical HJM model and discuss its predictive performance.

Language

en

Provenance

Recieved from ProQuest

File Size

102 p.

File Format

application/pdf

Rights Holder

Ebenezer Nkum

Included in

Mathematics Commons

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