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