IDEAS home Printed from
   My bibliography  Save this paper

Jackknifing Bond Option Prices


  • Jun Yu
  • Peter Phillips


In continuous time specifications, the prices of interest rate derivative securities depend crucially on the mean reversion parameter of the associated interest rate diffusion equation. This parameter is well known to be subject to estimation bias when standard methods like maximum likelihood (ML) are used. The estimation bias can be substantial even in very large samples and it translates into a bias in pricing bond options and other derivative securities that is important in practical work. The present paper proposes a very general and computationally inexpensive method of bias reduction for pricing bond options that is based on Quenouille's (1956) jackknife. We show how the method can be applied directly to the options price itself as well as the coefficients in continuous time models. The method is implemented and evaluated here in the Cox, Ingersoll and Ross (1985) model, although it has much wider applicability. A Monte Carlo study shows that the proposed procedure achieves substantial bias reductions in pricing bond options with only mild increases in variance that do not compromise the overall gains in mean squared error. Our findings indicate that bias correction in estimation of the drift can be more important in pricing bond options than correct specification of the diffusion. Thus, even if ML or approximate ML can be used to estimate more complicated models, it still appears to be of equal or greater importance to correct for the effects on pricing bond options of bias in the estimation of the drift. An empirical application to U.S. interest rates highlights the differences between bond and option prices implied by the jackknife procedure and those implied by the standard approach. These differences are large and suggest that bias reduction in pricing options is important in practical applications

Suggested Citation

  • Jun Yu & Peter Phillips, 2004. "Jackknifing Bond Option Prices," Econometric Society 2004 North American Winter Meetings 115, Econometric Society.
  • Handle: RePEc:ecm:nawm04:115

    Download full text from publisher

    File URL:
    File Function: main text
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Myerson, Roger B, 1983. "Mechanism Design by an Informed Principal," Econometrica, Econometric Society, vol. 51(6), pages 1767-1797, November.
    2. Marshall Robert C. & Meurer Michael J. & Richard Jean-Francois & Stromquist Walter, 1994. "Numerical Analysis of Asymmetric First Price Auctions," Games and Economic Behavior, Elsevier, vol. 7(2), pages 193-220, September.
    3. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
    5. Indranil Chakraborty & Georgia Kosmopoulou, 2004. "Auctions with shill bidding," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(2), pages 271-287, August.
    6. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
    7. Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994. "The Folk Theorem with Imperfect Public Information," Econometrica, Econometric Society, vol. 62(5), pages 997-1039, September.
    8. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    9. Matthews, Steven, 1987. "Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View," Econometrica, Econometric Society, vol. 55(3), pages 633-646, May.
    10. Mailath, George J. & Zemsky, Peter, 1991. "Collusion in second price auctions with heterogeneous bidders," Games and Economic Behavior, Elsevier, vol. 3(4), pages 467-486, November.
    11. Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
    12. Andreas Blume & Paul Heidhues, 2001. "Tacit Collusion in Repeated Auctions," CIG Working Papers FS IV 01-23, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
    13. Lebrun, Bernard, 1996. "Existence of an Equilibrium in First Price Auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 421-443, April.
    14. McAfee, R Preston & McMillan, John, 1992. "Bidding Rings," American Economic Review, American Economic Association, vol. 82(3), pages 579-599, June.
      • McAfee, R. Preston & McMillan, John., 1990. "Bidding Rings," Working Papers 726, California Institute of Technology, Division of the Humanities and Social Sciences.
    15. Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June.
    16. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    17. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    18. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-142, February.
    19. Marc S. Robinson, 1985. "Collusion and the Choice of Auction," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 141-145, Spring.
    20. Skrzypacz, Andrzej & Hopenhayn, Hugo, 2004. "Tacit collusion in repeated auctions," Journal of Economic Theory, Elsevier, vol. 114(1), pages 153-169, January.
    21. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    22. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    23. Lyk-Jensen, P., 1996. "Some Suggestions on How to Cheat the Auctioneer: Collusion in Auctions when Signals Are Affiliated," G.R.E.Q.A.M. 96a27, Universite Aix-Marseille III.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Bias Reduction; Option Pricing; Bond Pricing; Term Structure ofInterest Rate; Re-sampling; Estimation of Continuous Time Models.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecm:nawm04:115. 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: (Christopher F. Baum). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.