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  Issue 22 | Archive February 2015

Local-Momentum Autoregression and the Modeling of Interest Rate Term Structure

A paper by Duan Jin-Chuan (National University of Singapore)

RMI¡¯s Prof. Duan Jin-Chuan, also Cycle & Carriage Professor of Finance with NUS Business School, wrote a research paper entitled ¡°Local-Momentum Autoregression and the Modeling of Interest Rate Term Structure.¡±

This paper contributes to the econometric modeling of interest rates and the pricing of debt instruments by proposing a new 3-factor interest rate model. The model hinges on a novel local-momentum autoregression (LM-AR) process that tracks a stochastic central tendency. It is adopted as the global risk driver for interest rates. The LM-AR process proposed by Prof. Duan combines the typical mean-reversion term widely adopted in economics and finance with a new momentum term. The new model with only one extra parameter is parsimonious and can be easily made stationary. In short, stationarity and moment-running go hand-in-hand so that it becomes mean-reverting on a large timescale but shows local momentum on a smaller timescale. Local momentum can also be one of two types ¨C momentum-preserving and momentum-building.

The LM-AR model was motivated by observing US interest rates over a long time span. Local movement of interest rates tend to be small and directional, but over a longer time span interest rates show large variations through different phases of business cycle and/or over various interest rate policy regimes. Therefore, it is reasonable to conjecture that interest rates should exhibit the local momentum-building characteristic.

With the LM-AR process as the interest rate risk driver, Prof. Duan went on to derive a term structure model that theoretically links together interest rates of various maturities. The term structure model can be used for pricing, hedging and policy analysis. The term structure model can also serve as the basis for estimation involving interest rates of multiple maturities.

The paper¡¯s empirical study employs seven weekly series of US interest rates for different maturities from January 1954 to December 2013. The results strongly indicate the presence of local momentum, and it is particularly of the local momentum-building type as expected.

In conclusion, this paper adds to the vast literature of term structure of interest rates in a unique way. It offers an intuitive and parsimonious non-Markovian formulation of a general term structure model. Because the LM-AR model exhibits interesting endogenous cycles, the paper also opens up a new way for modeling many other economic time series.

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Editor: Ivy Wang (rmiwy@nus.edu.sg)