Models for Estimating the Structure of Interest Rates from Observations of Yield Curves

K. O. Kortanek1 and V. G. Medvedev2

https://kwel.biz.uiowa.edu/

ABSTRACT. We present a dynamical systems approach for modelling the term structure of interest rates based on a linear differential equation under uncertainty. Impulse or point-impulse perturbations are introduced on either
  1. the spot (shortest-term, risk neutral) interest rate as the unknown function, or
  2. its integral, namely the yield function, or
  3. both simultaneously.

Parameters are estimated by minimizing the maximum absolute value of the measurement errors, which is a nonlinear semi-infinite programming problem.

Beyond the learning period (the current time), the solved-for spot rate function becomes the forecast of the unobservable function in a future period, while its integral should approximate the yield function well.

Non-arbitrage is addressed by providing a sufficient condition under which non-arbitrage is guaranteed. The property of mean-reversion is also preserved, and functional estimates are provided for the market price of risk.

Analogous concepts to "drift" and "volatility" are treated in a manner that provides a criterion for the choice of perturbation to employ in a given real situation.

We test the approach empirically with daily Treasury yield curve rates data, mainly for discount bonds having 3 to 6 month maturities over observation periods of up to one year. Computational results are reported for many numerical experiments together with some financial interpretations: see https://kwel.biz.uiowa.edu/

1Department of Management Sciences
College of Business Administration
and Program in Applied Mathematical & Computational Sciences
University of Iowa
Iowa City, IA
USA 52242
email: ken-kortanek@uiowa.edu

2 Department of Optimal Control Methods
Faculty of Applied Mathematics & Informatics
Byelorussian State University, F. Skorina pr. 4
Republic Belarus

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