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The theory of interest rate arbitrage : review and extensions Dolf, Benedikt


The theory of interest rate arbitrage is the subject of this paper. Three objectives have guided the structure of the analysis. The first concerns the literature about interest arbitrage and the determination of the forward exchange rate. The contributions are numerous and diverse; a general consensus has not yet been reached. A critical survey of the literature is therefore undertaken with the aim of putting the various contributions into perspective. It is the contention underlying this part of the present paper that, diverse as the many models of interest arbitrage may be, they are all specific applications of Keynes' basic theory. In this sense, the evolution of theoretical thought about interest arbitrage can be seen as descending from the general to the specific. An important distinction is made, however. Keynes and his followers saw interest arbitrage as the major determinant of the forward rate. Modern economists, on the other hand, recognize that interest arbitrage is only one of many factors instrumental in the determination of the forward rate. Two apparently significant considerations have not received the attention they deserve in the literature. The first concerns the impact of arbitrage on interest rates; the other the existence of multiple interest differentials. The relationship between forward and interest rates has not been explored in depth in the literature. To investigate the impact of arbitrage on interest rates forms therefore the second objective of this study. It is contended that the relationship between foreign exchange rates and interest rates is of a different nature under different systems of exchange rate determination. Accordingly, Chapter III examines the impact of interest arbitrage on interest rates under pegged exchange rates; Chapter IV discusses the problem in a setting of flexible exchange rates. Under pegged exchange rates, money markets are directly affected by arbitrage. The relative variations of forward and interest rates are found to depend on the relative size of the respective markets. Small markets must absorb a greater amount of variation than do larger ones. Under flexible spot rates, the burden of adjustment is borne entirely by foreign exchange rates. The relative variation of spot versus forward rates depends again on the relative size of the two markets. Chapter IV has been expanded in order to investigate the consequences of an autonomous change in forward rates. The findings are contrasted with the results of an autonomous change in interest rates. This analysis solves a puzzling paradox to be found in the literature. Most models of interest arbitrage are based on the unrealistic assumption that a unique interest differential exists between any two markets. To examine the cognitive status of such models forms the third objective in this paper. It is concluded in Chapter V that conventional models apply only under very restrictive conditions. Specifically, it is required that one particular interest differential dominates all others in the sense that arbitragers concentrate their efforts exclusively on it. The alternative condition would be that the risk structures in two money markets are such that all interest differentials are identical at all times. These conditions are not bound to be realized in the real world. The predictions of simplified models are therefore not likely to be accurate both with respect to the level of the forward exchange rate and to the amount of funds transferred by arbitragers.

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