Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-27T23:09:03.097Z Has data issue: false hasContentIssue false
  • English
  • Français

A Discrete-Time Model for Reinvestment Risk in Bond Markets*

Published online by Cambridge University Press:  17 April 2015

Mikkel Dahl
Mikkel Dahl*
Affiliation:
Markets, Nordea Christiansbro, Strandgade 3, Postbox 850, DK-0900 Copenhagen C, Denmark, Email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we propose a discrete-time model with fixed maximum time to maturity of traded bonds. At each trading time, a bond matures and a new bond is introduced in the market, such that the number of traded bonds is constant. The entry price of the newly issued bond depends on the prices of the bonds already traded and a stochastic term independent of the existing bond prices. Hence, we obtain a bond market model for the reinvestment risk, which is present in practice, when hedging long term contracts. In order to determine optimal hedging strategies we consider the criteria of super-replication and risk-minimization.

Keywords

Zero coupon bondincomplete marketforward ratesrisk-minimizationsuper-replication
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 2 , November 2007 , pp. 235 - 264
Copyright
Copyright © ASTIN Bulletin 2007

Footnotes

*

JEL classification: G10.

Mathematics Subject Classification (2000): 62P05, 91B28.

References

Aliprantis, C.D., Polyrakis, Y. A. and Tourky, R. (2002) The cheapest hedge, Journal of Mathematical Economics 37, 269–295.CrossRefGoogle Scholar
Björk, T. (2004) Arbitrage Theory in Continuous Time, 2nd edn, Oxford University Press.CrossRefGoogle Scholar
Dahl, M. (2005) A Continuous-Time Model for Reinvestment Risk in Bond Markets, Working paper, Laboratory of Actuarial Mathematics, University of Copenhagen.Google Scholar
El Karoui, N. and Quenez, M.C. (1995) Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market, SIAM Journal on Control and Optimization 33, 29–66.CrossRefGoogle Scholar
Föllmer, H. and Schied, A. (2002) Stochaistic Finance: An Introduction in Discrete Time, de Gruyter Series in Mathematics 27, Berlin.CrossRefGoogle Scholar
Föllmer, H. and Schweizer, M. (1988) Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading, ASTIN Bulletin 18, 147–160.CrossRefGoogle Scholar
Harrison, J.M. and Kreps, D.M. (1979) Martingales and Arbitrage in Multiperiod Securities Markets, Journal of Economic Theory 20, 381–408.CrossRefGoogle Scholar
Harrison, J.M. and Pliska, S.R. (1981) Martingales and Stochaistic Integrals in the Theory of Continuous Trading. Stochaistic Processes and their Applications 11, 215–260.CrossRefGoogle Scholar
Jarrow, R. (1996) Modelling Fixed Income Securities and Interest Rate Options, The McGraw-Hill Companies Inc.Google Scholar
Møller, T. (2001) Hedging Equity-Linked Life Insurance Contracts, North American Actuarial Journal 5(2), 79–95.CrossRefGoogle Scholar
Musiela, M. and Rutkowski, M. (1997) Martingale Methods in Financial Modelling, Springer-Verlag, Berlin.CrossRefGoogle Scholar
Neuberger, A. (1999) Hedging Long-Term Exposures with Multiple Short-Term Futures Contracts, The Review of Financial Studies 12(3), 429–459.CrossRefGoogle Scholar
Rutkowski, M. (1999) Self-Financing Strategies for Sliding, Rolling-Horizon, and Consol Bonds, Mathematical Finance 9(4), 361–385.CrossRefGoogle Scholar
Schweizer, M. (1994) Risk-minimizing Hedging Strategies under Restricted Information, Mathematical Finance 4, 327–342.CrossRefGoogle Scholar
Schweizer, M. (1995) On the Minimal Martingale Measure and the Föllmer-Schweizer Decomposition, Stochastic Analysis and Applications 13, 573–599.CrossRefGoogle Scholar
Sommer, D. (1997) Pricing and Hedging of Contingent Claims in Term Structure Models with Exogenous Issuing of New Bonds, European Financial Management 3(3), 269–292.CrossRefGoogle Scholar