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Discrete-Time Interest Rate Modelling

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  • Lane P. Hughston
  • Andrea Macrina

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 provides 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 assets, 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, 2009. "Discrete-Time Interest Rate Modelling," Papers 0911.0750, arXiv.org.
  • Handle: RePEc:arx:papers:0911.0750
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