Working Paper: NBER ID: w8682
Authors: Ravi Jagannathan; Andrew Kaplin; Steve Guoqiang Sun
Abstract: We evaluate the classical Cox, Ingersoll and Ross (1985) (CIR) model using data on 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. In particular the pricing errors are related to the slope of the swap yield curve. 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 tends to overvalue shorter maturity caps and undervalue longer maturity caps. With only one or two factors, the model also tends to undervalue swaptions. Our findings point out the need for evaluating term structure models using data on derivative prices.
Keywords: Cox-Ingersoll-Ross model; LIBOR; swap rates; caps; swaptions
JEL Codes: C13; C32; C51; E43; G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| model parameters (C51) | observed LIBOR and swap rates (E43) |
| model misspecification (C52) | pricing errors in cap and swaption markets (G13) |
| model assumptions (C51) | dynamics of interest rate derivatives (E43) |
| model misspecification (C52) | overvaluation of shorter maturity caps (G19) |
| model misspecification (C52) | undervaluation of longer maturity caps (G19) |