Ben Bernanke praised the two factor mean reverting model first proposed by Beaglehole and Tenney in 1991. The history of this model is sketched below.

http://www.federalreserve.gov/boarddocs/speeches/2004/200401032/default.htm

Of course, basic financial theory implies that a link does exist between short-term interest rates, such as the federal funds rate, and longer-term rates, such as Treasury bond yields and mortgage rates. In particular, longer-term yields should depend in part on market expectations about the future course of short-term rates. For example, with the current setting of the funds rate held constant, any arriving news that leads bond market participants to expect higher future values of the funds rate will tend to raise bond yields and lower bond prices. The link between long-term bond yields and market expectations of future monetary policy actions is familiar to all financial-market participants and has been well supported by recent empirical research. For example, Antulio Bomfim has demonstrated that the shape of the term structure of Treasury yields can be effectively described by a two-factor model, in which the first factor corresponds to the current setting of the funds rate and the second factor closely approximates medium-term monetary policy expectations (Bomfim, 2003).

The fact that market expectations of future settings of the federal funds rate are at least as important as the current value of the funds rate in determining key interest rates such as bond and mortgage rates suggests a potentially important role for central bank communication: If effective communication can help financial markets develop more accurate expectations of the likely future course of the funds rate, policy will be more effective (in a precise sense that I will explain further soon), and risk in financial markets should be reduced as well.

Bomfim, Antulio (2003). “Monetary Policy and the Yield Curve,” Board of Governors of the Federal Reserve System, Finance and Economics Discussion Series 2003-15 (February).

The 1991 BT paper with the Double Decay model is cited by Nowman Babbs.

http://www.federalreserve.gov/pubs/feds/2003/200315/200315abs.html

Monetary Policy and the Yield Curve

Antulio N. Bomfim

2003-15The Modeling Framework

Consider the following model for the evolution of the short rate, r(t),dr(t) = k[theta(t) − r(t)]dt + vdW_r(t) (8)

dtheta(t) = alpha[beta − theta(t)]dt + dW_theta(t) (9)

r(t) is assumed to error-correct toward its time-varying central tendency

theta(t) with a mean reversion coefficient k. theta(t) is also assumed to follow a

mean-reverting process, with denoting its speed of mean reversion alpha and

its long-run value beta. dW_r(t) and dW_theta(t) are uncorrelated stochastic shocks

(infinitesimal increments to standard Brownian motions) hitting the short

rate and its central tendency, respectively, and v and are their volatilities.

In terms of the economics of the model, (t) can be thought of as where

market participants think the monetary authority will take the short rate

in the future, an implicit notion of a policy reaction function, and is the

steady-state value of the short rate.

The above model is a two-factor extension of the one-factor model originally

proposed by Vasicek (1977) and a variant of the double-mean reverting

framework discussed by Babbs and Nowman (1999) and the two-factor model

of Balduzzi et al. (1998). Equations (8) and (9) make up a system of stochastic

dierential equations, which can be solved to obtainhttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=142134

## Kalman Filtering of Generalized Vasicek Term Structure Models

## K. Ben Nowman

City University London## Simon H. Babbs

The Options Clearing Corporation

Journal of Financial and Quantitative Analysis, March 1999

Abstract:

We present a subclass of Langetieg’s (1980) linear Gaussian models of the term structure. The bond price is derived in terms of a finite set of state variables with correlated innovations. The subclass contains a reformulation of the double decay model of Beaglehole and Tenney (1991), enabling us to clarify interpretation of their parameters. We apply Kalman filtering to a state space formulation of the model allowing measurement errors in the data. One, two and three factor models are estimated on US data over 1987-1996 and the results indicate the subclass of models can fit the US term structure.

=Added Dec 5 2012

Bomfim cites the paper by Das et al instead of Beaglehole Tenney.

http://www.federalreserve.gov/pubs/feds/2003/200315/200315pap.pdf

http://www.federalreserve.gov/pubs/feds/2003/200315/200315abs.html

http://algo.scu.edu/~sanjivdas/BalduzziDasForesi_ReStat1998_CentralTendency.pdf

(My recollection is that David Beaglehole references giving a talk on his thesis and the BT work at NYU prior to the first NYU working paper.)

http://algo.scu.edu/~sanjivdas/

Note that Foresi was at Goldman Sachs and their 1998 paper was published by Harvard. That was during the investigation in US v. Harvard, Shleifer and Hay and while Russia was getting IMF loans from Larry Summers and Stanley Fischer.

Das has posted all the working paper versions of their paper at SSRN.

http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=17108

This makes it handy for the Indian, Pakistani, Chinese and Russian governments to review this history with these in one place. Very thoughtful.

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