An Evaluation of Multi-Factor Cir Models Using Libor, Swap Rates, and Cap and Swaption Prices

44 Pages Posted: 20 Dec 2001 Last revised: 25 Oct 2010

See all articles by Andrew Kaplin

Andrew Kaplin

Northwestern University - Kellogg School of Management

Steve Guoqiang Sun

University Capital Strategies Group

Ravi Jagannathan

Northwestern University - Kellogg School of Management; National Bureau of Economic Research (NBER); Shanghai Jiao Tong University (SJTU) - Shanghai Advanced Institute of Finance (SAIF); Indian School of Business (ISB), Hyderabad

Date Written: December 2001

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.

Suggested Citation

Kaplin, Andrew Serge and Sun, Steve Guoqiang and Jagannathan, Ravi, An Evaluation of Multi-Factor Cir Models Using Libor, Swap Rates, and Cap and Swaption Prices (December 2001). NBER Working Paper No. w8682. Available at SSRN: https://ssrn.com/abstract=294731

Andrew Serge Kaplin

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States
847-491-3838 (Phone)
847-491-5719 (Fax)

Steve Guoqiang Sun

University Capital Strategies Group

Minneapolis, MN
United States

Ravi Jagannathan (Contact Author)

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
429 Andersen Hall
Evanston, IL 60208
United States
847-491-8338 (Phone)
847-491-5719 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Shanghai Jiao Tong University (SJTU) - Shanghai Advanced Institute of Finance (SAIF) ( email )

Shanghai Jiao Tong University
211 West Huaihai Road
Shanghai, 200030
China

Indian School of Business (ISB), Hyderabad ( email )

Hyderabad, Gachibowli 500 019
India

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