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Discrete-Time Interest Rate Modelling

  • Lane P. Hughston

    ()

    (Department of Mathematics, Imperial College)

  • Andrea Macrina

    ()

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

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    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.

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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP691.pdf
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    Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 691.

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    Length: 7pages
    Date of creation: Jan 2010
    Date of revision:
    Handle: RePEc:kyo:wpaper:691
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