Term Structure of Interest Rates, Yield Curve Residuals, and the Consistent Pricing of Interest Rates and Interest Rate Derivatives
Dynamic term structure models (DTSMs) price interest rate derivatives based on the model implied fair values of the yield curve, ignoring any pricing residuals on the yield curve that are either from model approximations or market imperfections. In contrast, option pricing in practice often takes the market observed yield curve as given and focuses exclusively on the specification of the volatility structure of forward rates. Thus, if any errors exist on the observed yield curve, they will be carried over permanently. This paper proposes a new framework that consistently prices both interest rates and interest rate derivatives. In particular, under such a framework, instead of making a priori assumptions, we allow the data on interest rates and interest rate derivatives to dictate the dynamics of the yield curve residuals, as well as their impact on the pricing of interest rate derivatives. Specifically, we propose an m+ n model structure. The first m factors capture the systematic movement of the yield curve and hence are referred to as the yield curve factors. The latter n factors are derived from the residuals on the yield curve and are labeled as the residual factors. We estimate a simple 3+3 Gaussian affine example using eight years of data on U.S. dollar LIBOR/swap rates and interest rate caps. The model performs well in pricing both interest rates and interest rate derivatives. Furthermore, we find that small residuals on the yield curve can have large impacts on the pricing of interest rate caps. Under the estimated model, the three Gaussian yield curve factors explain over 99.5 percent of the variation on the yield curve, but only account for less than 25 percent of the variation in the cap implied volatility. Incorporating the three residual factors improves the explained variance in cap implied volatility to over 95 percent. We investigate the reasons behind the ``amplification'' of yield curve residuals in pricing interest rate derivatives and find that the yield curve residuals are a recurring phenomenon, not a onetime event. Hence, the dynamics of the residuals influence option prices even if the current residual level is zero. We also find that the residuals concentrate on the two ends of the yield curve and are more transient than the original interest rate series, both of which, we argue, contribute to the amplification effect.
|Date of creation:||30 Aug 2002|
|Date of revision:||05 Sep 2002|
|Note:||Type of Document - pdf; prepared on MikTex; to print on postscript; pages: 37 ; figures: included. produced via dvipdfm|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- D. Duffie & D. Filipovic & W. Schachermayer, 2002. "Affine Processes and Application in Finance," NBER Technical Working Papers 0281, National Bureau of Economic Research, Inc.
- Duffee, Gregory R, 1999.
"Estimating the Price of Default Risk,"
Review of Financial Studies,
Society for Financial Studies, vol. 12(1), pages 197-226.
- Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
- Duan, Jin-Chuan & Simonato, Jean-Guy, 1999.
"Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter,"
Review of Quantitative Finance and Accounting,
Springer, vol. 13(2), pages 111-35, September.
- Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Estimating and Testing Exponential Affine Term Structure Models by Kalman Filter," CIRANO Working Papers 95s-44, CIRANO.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997.
" Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,"
Journal of Finance,
American Finance Association, vol. 52(1), pages 409-30, March.
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
- Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
- Massoud Heidari & Liuren WU, 2002. "Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates?," Finance 0207013, EconWPA.
- Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
- Rong Fan & Anurag Gupta & Peter Ritchken, 2003. "Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets," Journal of Finance, American Finance Association, vol. 58(5), pages 2219-2248, October.
- Goldstein, Robert S, 2000. "The Term Structure of Interest Rates as a Random Field," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 365-84.
- Liu, Jun & Longstaff, Francis A. & Mandell, Ravit E., 2000.
"The Market Price of Credit Risk: An Empirical Analysis of Interest Rate Swap Spreads,"
University of California at Los Angeles, Anderson Graduate School of Management
qt0zw4f9w6, Anderson Graduate School of Management, UCLA.
- Jun Liu & Francis A. Longstaff & Ravit E. Mandell, 2002. "The Market Price of Credit Risk: An Empirical Analysis of Interest Rate Swap Spreads," NBER Working Papers 8990, National Bureau of Economic Research, Inc.
- Pierre Collin-Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, 08.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Knez, Peter J & Litterman, Robert & Scheinkman, Jose Alexandre, 1994. " Explorations into Factors Explaining Money Market Returns," Journal of Finance, American Finance Association, vol. 49(5), pages 1861-82, December.
- Ravi Jagannathan & Andrew Kaplin & Steve Guoqiang Sun, 2001.
"An Evaluation of Multi-Factor CIR Models Using LIBOR, Swap Rates, and Cap and Swaption Prices,"
NBER Working Papers
8682, National Bureau of Economic Research, Inc.
- Jagannathan, Ravi & Kaplin, Andrew & Sun, Steve, 2003. "An evaluation of multi-factor CIR models using LIBOR, swap rates, and cap and swaption prices," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 113-146.
- Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
- Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02.
- Francis A. Longstaff, 2001. "The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence," Journal of Finance, American Finance Association, vol. 56(6), pages 2067-2109, December.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpfi:0207010. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.