Cox-Ingersoll-Ross model

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The Cox-Ingersoll-Ross model in finance is a mathematical model describing the evolution of interest rates. It is a type of "one factor model" (Short rate model) as describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives. It was introduced in 1985 by John C. Cox, Jonathan E. Ingersoll and Stephen A. Ross as an extension of the Vasicek model.

The model specifies that the instantaneous interest rate follows the stochastic differential equation:

dr_t = a(b-r_t)\, dt + \sigma\sqrt{r_t}\, dW_t

where Wt is a Wiener process modelling the random market risk factor.

The drift factor, a(b − rt), is exactly the same as in the Vasicek model. It ensures mean reversion of the interest rate towards the long run value b, with speed of adjustment governed by the strictly positive parameter a.

The standard deviation factor, \sigma \sqrt{r_t}, corrects the main drawback of Vasicek's model, ensuring that the interest rate can not become negative. Thus, at low values of the interest rate, the standard deviation becomes close to zero, cancelling the effect of the random shock on the interest rate. Consequently, when the interest rate gets close to zero, its evolution becomes dominated by the drift factor, which pushes the rate upwards (towards equilibrium).

[edit] References

  • Hull, John C. (2003). Options, Futures and Other Derivatives. Upper Saddle River, NJ: Prentice Hall. ISBN 0130090565.
  • Cox, J.C., J.E. Ingersoll and S.A. Ross (1985). "A Theory of the Term Structure of Interest Rates". Econometrica 53: 385-407.
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