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The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence

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  • Longstaff, Francis A
  • Santa-Clara, Pedro
  • Schwartz, Eduardo S
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    Abstract

    Although traded as distinct products, caps and swaptions are linked by no-arbitrage relations through the correlation structure of interest rates. Using a string market model framework, we solve for the correlation matrix implied by the swaptions market and examine the relative valuation of caps and swaptions. The results indicate that swaption prices are generated by four factors and that implied correlations are generally lower than historical correlations. We find evidence that long-dated swaptions are priced inconsistently and that there were major distortions in the swaptions market during the hedge-fund crisis of late 1998. We also find that cap prices periodically deviate significantly from the no-arbitrage values implied by the swaptions market.

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    Paper provided by Anderson Graduate School of Management, UCLA in its series University of California at Los Angeles, Anderson Graduate School of Management with number qt65f1914p.

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    Date of creation: 01 Sep 2000
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    Handle: RePEc:cdl:anderf:qt65f1914p

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    1. D. P. Kennedy, 1997. "Characterizing Gaussian Models of the Term Structure of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 107-118.
    2. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    3. Litzenberger, Robert H, 1992. " Swaps: Plain and Fanciful," Journal of Finance, American Finance Association, vol. 47(3), pages 831-50, July.
    4. Bicksler, James & Chen, Andrew H, 1986. " An Economic Analysis of Interest Rate Swaps," Journal of Finance, American Finance Association, vol. 41(3), pages 645-55, July.
    5. D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258.
    6. Anurag Gupta & Marti G. Subrahmanyam, 1999. "An Empirical Examination of the Convexity Bias in the Pricing of Interest Rate Swaps," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-001, New York University, Leonard N. Stern School of Business-.
    7. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    8. Driessen, Joost & Klaassen, Pieter & Melenberg, Bertrand, 2003. "The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(03), pages 635-672, September.
    9. 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.
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    11. 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.
    12. Sun, Tong-sheng & Sundaresan, Suresh & Wang, Ching, 1993. "Interest rate swaps: An empirical investigation," Journal of Financial Economics, Elsevier, vol. 34(1), pages 77-99, August.
    13. de Jong, Frank & Santa-Clara, Pedro, 1999. "The Dynamics of the Forward Interest Rate Curve: A Formulation with State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 131-157, March.
    14. Liu, Jun & Longstaff, Francis A, 2000. "Losing Money on Arbitrages: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities," University of California at Los Angeles, Anderson Graduate School of Management qt48k8f97f, Anderson Graduate School of Management, UCLA.
    15. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
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    17. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    18. Duffie, Darrell & Singleton, Kenneth J, 1997. " An Econometric Model of the Term Structure of Interest-Rate Swap Yields," Journal of Finance, American Finance Association, vol. 52(4), pages 1287-1321, September.
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    Cited by:
    1. Matthew Pritsker, 2005. "Large investors: implications for equilibrium asset, returns, shock absorption, and liquidity," Finance and Economics Discussion Series 2005-36, Board of Governors of the Federal Reserve System (U.S.).
    2. Qiang Dai & Kenneth J. Singleton, 2001. "Expectation Puzzles, Time-varying Risk Premia, and Dynamic Models of the Term Structure," NBER Working Papers 8167, National Bureau of Economic Research, Inc.
    3. 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.
    4. 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.

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