Interest Rate Options in Multifactor Cox-Ingersoll-Ross Models of the Term Structure

Abstract

We examine valuation of interest rate options in multifactor versions of the Cox-Ingersoll-Ross model, including European options on discount bonds, European options on Eurodollar futures, and caps on floating interest rates. Valuation models for options on coupon bonds and coupon bond futures are also discussed. Standard solution techniques for such problems require numerical integration of a joint probability distribution, which becomes exceedingly time-consuming when there are more than two factors. We describe an alternative approach based on Fourier inversion methods that is much more efficient for solving multifactor models. In one example, using a three- factor model to price interest rate caps, our procedure reduces computation time from 2.83 hours to 1.93 seconds. Using this approach, we show that multifactor Cox-Ingersoll- Ross models generate prices for interest rate options that differ significantly from prices generated by Black's model when options with long-term expirations are valued. When a multifactor model is used for hedging, the hedge portfolio requires additional securities, and conventional formulas for hedge ratios must be modified.