An evaluation of multi-factor CIR models using LIBOR, swap rates, and cap and swaption prices

We evaluate the classical Cox et al. (Econometrica 53(2) (1985) 385) (CIR) model using data on London Interbank Offer Rate (LIBOR), swap rates and caps and swaptions. With three factors the CIR model is able to fit the term structure of LIBOR and swap rates rather well. The model is able to match the hump shaped unconditional term structure of volatility in the LIBOR-swap market. However, statistical tests indicate that the model is misspecified. The economic importance of these shortcomings is highlighted when the model is confronted with data on cap and swaption prices. Pricing errors are large relative to the bid-ask spread in these markets. The model overvalues shorter maturity caps and undervalues longer maturity caps. The model tends to undervalue swaptions. The magnitude of the mispricing is positively related to the magnitude of the slope of the yield curve. Our findings point out the need for evaluating term structure models using data on derivative prices.