Yield Curve Smoothing and Residual Variance of Fixed Income Positions

Raphael Douady ()

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

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 optimise a criterion depending on transaction costs and residual variance

Keywords: Interest rate models; arbitrage pricing; infinite dimensional models; Martingale methods (search for similar items in EconPapers)
JEL-codes: G12 (search for similar items in EconPapers)
Pages: 41 pages
Date: 2014-12
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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ftp://mse.univ-paris1.fr/pub/mse/CES2014/14091.pdf (application/pdf)

Related works:
Working Paper: Yield Curve Smoothing and Residual Variance of Fixed Income Positions (2014)
Working Paper: Yield Curve Smoothing and Residual Variance of Fixed Income Positions (2014)
Working Paper: Yield Curve Smoothing and Residual Variance of Fixed Income Positions (2013)
Working Paper: Yield Curve Smoothing and Residual Variance of Fixed Income Positions (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:14091

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