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Long-Term Returns in Stochastic Interest Rate Models: Applications
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- Journal:
- ASTIN Bulletin: The Journal of the IAA / Volume 30 / Issue 1 / May 2000
- Published online by Cambridge University Press:
- 29 August 2014, pp. 123-140
- Print publication:
- May 2000
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- Article
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We extend the Cox-Ingersoll-Ross (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have studied the convergence of the long-term return by using the theory of generalised Bessel-square processes. We emphasize the applications of the convergence results. A limit theorem proves evidence of the use of a Brownian motion with drift instead of the integral
. For practice, however, this approximation turns out to be only appropriate when there are no explicit formulae and calculations are very time-consuming.
. For practice, however, this approximation turns out to be only appropriate when there are no explicit formulae and calculations are very time-consuming.