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Discrete-Time Interest Rate Modelling

Author

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  • Lane P. Hughston

    () (Department of Mathematics, Imperial College)

  • Andrea Macrina

    () (Department of Mathematics, King's College London, Institute of Economic Research, Kyoto University)

Abstract

This paper presents an axiomatic scheme for interest rate models in discrete time. We take a pricing kernel approach, which builds in the arbitrage-free property and pro- vides a link to equilibrium economics. We require that the pricing kernel be consistent with a pair of axioms, one giving the inter-temporal relations for dividend-paying as- sets, and the other ensuring the existence of a money-market asset. We show that the existence of a positive-return asset implies the existence of a previsible money-market account. A general expression for the price process of a limited-liability asset is derived. This expression includes two terms, one being the discounted risk-adjusted value of the dividend stream, the other characterising retained earnings. The vanishing of the latter is given by a transversality condition. We show (under the assumed axioms) that, in the case of a limited-liability asset with no permanently-retained earnings, the price process is given by the ratio of a pair of potentials. Explicit examples of discrete-time models are provided.

Suggested Citation

  • Lane P. Hughston & Andrea Macrina, 2010. "Discrete-Time Interest Rate Modelling," KIER Working Papers 691, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:691
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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP691.pdf
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    Keywords

    Interest rates models; pricing kernels; financial time series; Flesaker-Hughston models; transversality condition; financial bubbles;

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