The performance of multi-factor term structure models for pricing and hedging caps and swaptions

In this paper we empirically compare a wide range of different term structure models when it comes to the pricing and, in particular, hedging of caps and swaptions. We analyze the influence of the number of factors on the hedging and pricing results, and investigate which type of data "interest rate data or derivative price data" should be used to estimate the model parameters to obtain the best hedging and pricing results. We use data on interest rates, and cap and swaption prices from 1995 to 1999. The empirical results on the hedging of caps and swaptions show that, if the number of hedge instruments is equal to the number of factors, the multi-factor models outperform one-factor models in hedging caps and swaptions. However, if one uses a large set of hedge instruments, one-factor models perform as well as multi-factor models. In terms of pricing, we find that models with two or three factors imply better out-of-sample predictions of cap and swaption prices than one-factor models. Also, estimation on the basis of current derivative prices leads to more accurate out-of-sample prediction of cap and swaption prices than estimation on the basis of interest rate data.