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    Bank of Canada Banque du Canada

    Working Paper 2000-17 / Document de travail 2000-17

    A Practical Guide to Swap Curve Construction

    by

    Uri Ron

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    ISSN 1192-5434

    Printed in Canada on recycled paper

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    Bank of Canada Working Paper 2000-17

    August 2000

    A Practical Guide to Swap Curve Construction

    by

    Uri Ron

    Financial Markets DepartmentBank of Canada

    Ottawa, Ontario, Canada K1A [email protected]

    The views expressed in this paper are those of the author. No responsibilityfor them should be attributed to the Bank of Canada.

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    Contents

    Acknowledgments.......................................................................................................................... iv

    Abstract/Rsum..............................................................................................................................v

    1 Introduction.................................................................................................................................1

    2 The Swap Curve Advantage .......................................................................................................2

    3 Swap Curve Construction ...........................................................................................................4

    3.1 Curve inputs .............................................................................................................................4

    3.2 Deriving the swap curve ..........................................................................................................5

    3.2.1 The short end of the swap curve ...........................................................................................6

    3.2.2 The middle area of the swap curve .......................................................................................6

    3.2.3 The long end of the swap curve...........................................................................................10

    3.3 Interpolation algorithm ..........................................................................................................11

    3.3.1 Piecewise linear interpolation ............................................................................................12

    3.3.2 Piecewise cubic spline interpolation ..................................................................................12

    3.4 Consolidation.........................................................................................................................14

    4 Conclusions...............................................................................................................................15

    References......................................................................................................................................16

    Appendix 1.....................................................................................................................................18

    Appendix 2.....................................................................................................................................20

    iii

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    iv

    Acknowledgments

    I am grateful to Shafiq Ebrahim, John Kiff, Peter Thurlow, Pascal Farahmand, Walter Engert, RonMorrow, David Bolder, and Ginette Crew for helpful comments and suggestions.

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    v

    Abstract

    The swap market has enjoyed tremendous growth in the last decade. With government issuesshrinking in supply and increased price volatilities, the swap term structure has emerged as analternative pricing, benchmark, and hedging mechanism to the government term structure. This

    paper outlines the advantages of using the swap curve, and provides a detailed methodology forderiving the swap term structure for marking to market fixed-income products. The paperconcludes with a discussion of the proposed swap term structure derivation technique.

    JEL classification: G12, G15Bank classification: Asset pricing; International financial markets

    Rsum

    Le march des swaps a connu un essor prodigieux durant les annes 1990. Avec la rduction de

    loffre des titres dtat et la volatilit accrue de leurs prix, la structure terme des taux de swapsoffre une solution de rechange celle des emprunts dtat, tablissant ainsi une nouvelle courbede rfrence pour lvaluation des titres revenu fixe et la couverture des risques. Lauteur dcritles avantages que prsente lutilisation de la courbe des taux de swaps et expose en dtail unemthode permettant de dterminer celle-ci pour fins dvaluation des prix au march des titres revenu fixe. Lauteur conclut sur une discussion de la mthode quil propose.

    Classification JEL : G12, G15Classification de la Banque : valuation des actifs; Marchs financiers internationaux

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    0 20 40 60 80 100 1206.2

    6.4

    6.6

    6.8

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    7.2

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    Rate(%)

    Month

    Linear interpolationPiecewise cubic spline

    Spline forward curveLinear forward curve

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    0 20 40 60 80 100 1200

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    1.5

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    Linear interpolationPiecewise cubic splineSpline forward curve

    Linear forward curve

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    0 20 40 60 80 100 1203.5

    4

    4.5

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    Month

    Linear interpolationPiecewise cubic splineSpline forward curve

    Linear forward curve

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    0 20 40 60 80 100 1205.4

    5.6

    5.8

    6

    6.2

    6.4

    6.6

    6.8

    7

    Rate(%)

    Month

    Linear interpolationPiecewise cubic splineSpline forward curve

    Linear forward curve

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    0 20 40 60 80 100 1200

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    CAD

    EUR

    JPY

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    Bank of Canada Working Papers

    Documents de travail de la Banque du CanadaWorking papers are generally published in the language of the author, with an abstract in both official lan-

    guages.Les documents de travail sont publis gnralement dans la langue utilise par les auteurs; ils sont

    cependant prcds dun rsum bilingue.

    2000

    2000-16 Volatility Transmission Between Foreign Exchangeand Money Markets S.K. Ebrahim

    2000-15 Private Capital Flows, Financial Development, and EconomicGrowth in Developing Countries J.N. Bailliu

    2000-14 Employment Effects of Nominal-Wage Rigidity: An ExaminationUsing Wage-Settlements Data U.A. Faruqui

    2000-13 Fractional Cointegration and the Demand for M1 G. Tkacz

    2000-12 Price Stickiness, Inflation, and Output Dynamics: ACross-Country Analysis H. Khan

    2000-11 Identifying Policy-makers Objectives: An Application to theBank of Canada N. Rowe and J. Yetman

    2000-10 Probing Potential Output: Monetary Policy, Credibility, and OptimalLearning under Uncertainty J. Yetman

    2000-9 Modelling Risk Premiums in Equity and Foreign Exchange Markets R. Garcia and M. Kichian

    2000-8 Testing the Pricing-to-Market Hypothesis: Case of the TransportationEquipment Industry L. Khalaf and M. Kichian

    2000-7 Non-Parametric and Neural Network Models of Inflation Changes G. Tkacz

    2000-6 Some Explorations, Using Canadian Data, of theS-Variable inAkerlof, Dickens, and Perry (1996) S. Hogan and L. Pichette

    2000-5 Estimating the Fractional Order of Integration of Interest RatesUsing a Wavelet OLS Estimator G. Tkacz

    2000-4 Quelques rsultats empiriques relatifs lvolution du taux de changeCanada/tats-Unis R. Djoudad and D. Tessier

    2000-3 Long-Term Determinants of the Personal Savings Rate: Literature Reviewand Some Empirical Results for Canada G. Brub and D. Ct

    2000-2 GAUSSTM Programs for the Estimation of State-Space Models withARCH Errors: A Users Guide M. Kichian

    2000-1 The Employment Costs of Downward Nominal-Wage Rigidity J. Fars and S. Hogan

    Copies and a complete list of working papers are available from:Pour obtenir des exemplaires et une liste complte des documents de travail, prire de sadresser :

    Publications Distribution, Bank of Canada Diffusion des publications, Banque du Canada