Abstract
The purposes of this paper are to describe some results about the term structure of interest rates as stochastic processes, and to extend to this topic some of the author’s earlier results on stochastic processes. It is assumed that the instantaneous borrowing and lending rate (the spot rate) is modelled by a stochastic process which is both Markovian and Gaussian. Among such processes, the Ornstein-Uhlenbeck stochastic process is used. It has the advantage of being able to model phenomena which react to offset excessive movements in any one direction. Probabilities that the spot rates will deviate from the long term mean by more than preassigned boundary functions during various time intervals are obtained. The boundary functions are of the form Aσ or A<(l + R)t, 0 ≤ t ≤ T. Knowledge of such probabilities is needed for some applications of immunization theory.
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Beekman, J.A. (1987). Ornstein-Uhlenbeck Stochastic Processes Applied to Immunization. In: MacNeill, I.B., Umphrey, G.J., Chan, B.S.C., Provost, S.B. (eds) Actuarial Science. The University of Western Ontario Series in Philosophy of Science, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4796-2_11
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DOI: https://doi.org/10.1007/978-94-009-4796-2_11
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