Discrete-Time Interest-Rate Modelling

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Hughston, L P and Macrina, A. 2010. Discrete-Time Interest-Rate Modelling. In: M Ruzhansky and J Wirth, eds. Progress in Analysis and its Applications: Proceedings of the 7th International ISAAC Congress. Singapore: World Scientific Publishing Company, pp. 417-423. ISBN 9789814313162 [Book Section]

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Official URL: https://www.worldscientific.com/doi/10.1142/978981...

Abstract or Description

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.

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Book Section

Identification Number (DOI):

https://doi.org/10.1142/9789814313179_0054