Yield Curve Smoothing and Residual Variance of Fixed Income Positions

Raphaël Douady ()
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Raphaël Douady: Univ. Paris 1, CES

A chapter in Inspired by Finance, 2014, pp 221-256 from Springer

Abstract: Abstract We model the yield curve in any given country as an object lying in an infinite-dimensional Hilbert space, the evolution of which is driven by what is known as a cylindrical Brownian motion. We assume that volatilities and correlations do not depend on rates (which hence are Gaussian). We prove that a principal component analysis (PCA) can be made. These components are called eigenmodes or principal deformations of the yield curve in this space. We then proceed to provide the best approximation of the curve evolution by a Gaussian Heath–Jarrow–Morton model that has a given finite number of factors. Finally, we describe a method, based on finite elements, to compute the eigenmodes using historical interest rate data series and show how it can be used to compute approximate hedges which optimize a criterion depending on transaction costs and residual variance.

Keywords: Cylindrical Brownian motion; Term structure of interest rates; Yield curve; Heath–Jarrow–Morton model; Fixed-income models; Asymptotic arbitrage; 91G30; 91G60 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-02069-3_10

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DOI: 10.1007/978-3-319-02069-3_10

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