Interest rate volatility prior to monetary union under alternative pre-switch regimes

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1 Interest rate volatility prior to monetary union under alternative pre-switch regimes Bernd Wilfling HWWA DISCUSSION PAPER 143 Hamburgisches Welt-Wirtschafts-Archiv (HWWA) Hamburg Institute of International Economics 2001 I SSN

2 The HWWA is a member of: Wissenschaftsgemeinschaft Gottfried Wilhelm Leibniz (WGL) Arbeitsgemeinschaft deutscher wirtschaftswissenschaftlicher Forschungsinstitute (ARGE) Association d Instituts Européens de Conjoncture Economique (AIECE)

3 Interest rate volatility prior to monetary union under alternative pre-switch regimes Bernd Wilfling The paper is part of the International Financial Markets Research Programme of the HWWA.

4 HWWA DISCUSSION PAPER Edited by the PRESIDENTIAL DEPARTMENT Hamburgisches Welt-Wirtschafts-Archiv (HWWA) Hamburg Institute of International Economics Öffentlichkeitsarbeit Neuer Jungfernstieg Hamburg Telefon: 040/ Telefax: 040/ Internet: Bernd Wilfling Telefon: 040/

5 Contents Summary 6 Zusammenfassung 6 1 Introduction 7 2 Preliminaries, previous results, model setup Exchange rate dynamics The interest rate differential 11 3 Regime-comparison and implications Measuring the volatility of interest rate differentials Pre-switch regime comparison The free-float regime The managed-float regime Implications and empirical issues 22 4 Concluding remarks 24 References 26 List of Figures Figure 1 Infinitesimal variance paths under a free-float pre-switch regime 16 Figure 2 Variance paths under a managed-float pre-switch regime ( low η-value) 20 Figure 3 Variance paths under a managed-float pre-switch regime ( high η-value) 21 Figure 4 Crossing variance paths with alternative terms 22 Figure 5 Crossing variance paths for alternative η-values 23 5

6 Summary The volatility of interest rates is relevant for many financial applications. Under realistic assumptions the term structure of interest rate differentials provides an important prediction of the term structure of interest rates. This paper derives the term structure of differentials in a situation in which two open economies plan to enter a monetary union in the future. Two systems of floating exchange rates prior to the union are considered, namely a free-float and a managed-float regime. The volatility processes of arbitraryterm differentials under the respective pre-switch arrangements are compared. The paper elaborates the singularity of extremely short-term (i.e. instantaneous) interest rates under extensive leaning-against-the-wind intervention policies and discusses empirical issues. Zusammenfassung Die Volatilität von Zinssätzen ist für viele Anwendungen aus den Bereichen der Finanzund Geldtheorie von Bedeutung. Unter realistischen Bedingungen liefert die zeitliche Struktur von Zinsdifferentialen eine wichtige Vorhersage für die Zinsstruktur. Diese Arbeit leitet die Zinsdifferentialstruktur in einer Situation her, in der zwei offene Volkswirtschaften in der Zukunft eine Währungsunion bilden wollen. Es werden zwei alternative Wechselkursregime vor der Währungsunion betrachtet und zwar ein Reiner sowie ein Gemanagter Float. Das Papier vergleicht die Volatilitätsprozesse von Zinsdifferentialen beliebiger Fristigkeit unter den verschiedenen Wechselkurssystemen. Ferner stellt die Arbeit die singuläre Stellung extrem kurzfristiger (sogenannter instantaner) Zinssätze unter intensiven leaning-against-the-wind Interventionspolitiken heraus und diskutiert empirische Aspekte. JEL classifications: E43, F31, F33, C52 Key words: Interest rate volatility, term structure, exchange rate arrangements, intervention policy, stochastic processes 6

16 5 4 τ 0 infinitesimal variance 3 2 τ = 1.5 τ = time t Structural parameters: α = 1, σ = 2, ta = 0.5, ts = 2.5

20 5 4 τ 0 infinitesimal variance 3 2 τ = 1.0 τ = time t Structural parameters: η = 0.1, α = 1, σ = 2, ta = 0.5, ts = 2.5

21 5 4 τ 0 infinitesimal variance τ = 1.0 τ = time t Structural parameters: η = 2, α = 1, σ = 2, ta = 0.5, ts = 2.5

22 0.02 difference of variance-paths ν 2 {ID MF,1 }(,, τ = 0.05) ν 2 {ID MF,1 }(,, τ = 0.1) time t Structural parameters: η = 0.5, α = 1, σ = 2, t A = 0.5, t S = 2.5

23 2.0 η 1 = 1.0 infinitesimal variance η 3 = 3.0 η 2 = time t Structural parameters: α = 1, σ = 2, τ = 0.5, t A = 0.5, t S = 2.5

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