A FAMILY OF TERM‐STRUCTURE MODELS FOR LONG‐TERM RISK MANAGEMENT AND DERIVATIVE PRICING

Andrew J. G. Cairns

Mathematical Finance, 2004, vol. 14, issue 3, 415-444

Abstract: In this paper we propose a new family of term‐structure models based on the Flesaker and Hughston (1996) positive‐interest framework. The models are Markov and time homogeneous, with correlated Ornstein‐Uhlenbeck processes as state variables. We provide a theoretical analysis of the one‐factor model and a thorough emprical analysis of the two‐factor model. This allows us to identify the key factors in the model affecting interest‐rate dynamics. We conclude that the new family of models should provide a useful tool for use in long‐term risk management. Suitably parameterized, they can satisfy a wide range of desirable criteria, including: • sustained periods of both high and low interest rates similar to the cycle lengths we have observed over the course of the 20th century in the United Kingdom and the United States • realistic probabilities of both high and low interest rates consistent with historical data and without the need for regular recalibration • a wide range of shapes of yield curves, again consistent with what we have observed in the past and including the recent Japanese yield curve.

Date: 2004
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