Importance of mean-reversion of interest rate processes for options: The example of range warrants

Despite its well-known limitations, Black's model is often used in practice to value interest rate derivatives. The aim of this article is to analyse whether Black's approach, which models one specific forward rate rather than the whole yield curve, is also an appropriate solution for valuing interest rate range warrants. As the buyer of such a security is entitled to a payment at maturity with an amount depending on the number of days the reference interest rate lies within a specified range, the value of this instrument depends intuitively on the intensity of mean-reversion in interest rates. The valuation results of Black's model, which does not reflect the mean-reversion observed in the interest rate data, are compared with the results of a more sophisticated approach.