Practical Guide to Build Swap Curve

8/6/2019 Practical Guide to Build Swap Curve

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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

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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

7

7.2

7.4

7.6

7.8

Rate(%)

Month

Linear interpolationPiecewise cubic spline

Spline forward curveLinear forward curve


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0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

Rate(%)

Month

Linear interpolationPiecewise cubic splineSpline forward curve

Linear forward curve


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0 20 40 60 80 100 1203.5

4

4.5

5

5.5

6

6.5

Rate(%)

Month




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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




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0 20 40 60 80 100 1200

1

2

3

4

5

6

7

8

Rate(%)

Month

USD

CAD

EUR

JPY

0 20 40 60 80 100 1200

1

2

3

4

5

6

7

8

Rate(%)

Month

USD

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 Canada234 Wellington Street Ottawa Ontario K1A 0G9 234 rue Wellington Ottawa (Ontario) K1A 0G9