Applying Heath-Jarrow-Morton Model to Forecasting the US Treasury Daily Yield Curve Rates

The Heath-Jarrow-Morton (HJM) model is a powerful instrument for describing the stochastic evolution of interest rate curves under no-arbitrage assumption. An important feature of the HJM approach is the fact that the drifts can be expressed as functions of respective volatilities and the underlying correlation structure. Aimed at researchers and practitioners, the purpose of this article is to present a self-contained, but concise review of the abstract HJM framework founded upon the theory of interest and stochastic partial differential equations in infinite dimensions. To illustrate the predictive power of this theory, we apply it to modeling and forecasting the US Treasury daily yield curve rates. We fit a non-parametric model to real data available from the US Department of the Treasury and illustrate its statistical performance in forecasting future yield curve rates.

Forward Rate Models

In this chapter we study the Heath–Jarrow–Morton framework for forward rate models. Building on results from the previous chapter, the HJM drift condition is derived, some examples are studied, and the general Gaussian HJM model is analyzed in detail. The Musiela parameterization of forward rates is introduced and discussed in the context of infinite dimensional SDEs.

Pricing the Deflation Protection Option in TIPS Using an HJM Model with Inflation- and Interest-Rate Jumps

Much known about Treasury inflation-protected securities (TIPS) is related to the hedge they offer against inflation, but little is known about their protection against deflation—in the form of a deflation protection option (DPO). In this article, a pricing framework that builds on a Heath–Jarrow–Morton forward-rate economy with codependent inflation- and interest-rate jumps is derived to value this embedded DPO. The model prices for TIPS resulting from this pricing framework are found to most closely fit the 10-year notes issued following the 2008 crisis. Considering these notes accounted for over 70% of the total TIPS-market trading activity, this result underscores the importance of properly assessing DPO value in times of deflationary fears compounded by rising real yields, negligence of which may well be liable for the post-crisis mispricing in TIPS.

Um Modelo Unificado para a Previsão da Estrutura a Termo de Taxa de Juros

The focus of the paper is to present a new methodology for forecasting the Term Structure of Interest Rates (ETTJ). The objective is to answer the question: given the ETTJ curve at any given time, what is the ETTJ at a future date? Thus, we seek to construct an analytical expression for the prediction of an entire curve and not only for a given future price of any asset. This objective requires a predominantly analytical and theoretical approach rather than empirical or econometric. The characteristic of this approach is the development of a "hybrid" model, describing the evolution and dynamics of the ETTJ curve over time, combining three elements: a particular version of the HJM model, the Nelson-Siegel-Svensson parameterization, and an independent modeling of the short-term rate, via Hull-White model. As results are obtained analytical expressions for quantities of importance in the fixed income markets. Not being the focus of this work, the empirical evaluation appears only as an illustration, and a more rigorous empirical analysis is left for another article.