Jackknifing Bond Option Prices

Peter Phillips and Jun Yu

No 1392, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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 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.

Keywords: Bias Reduction; Option Pricing; Bond Pricing; Term Structure of Interest Rate; Re-sampling; Estimation of Continuous Time Models (search for similar items in EconPapers)
JEL-codes: C13 C22 E43 G13 (search for similar items in EconPapers)
Pages: 51 pages
Date: 2003-01
New Economics Papers: this item is included in nep-cfn, nep-cmp, nep-ecm, nep-fmk and nep-rmg
Note: CFP 1119.
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Citations: View citations in EconPapers (3)

Published in Review of Financial Studies (2005), 18(2): 707-742

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Journal Article: Jackknifing Bond Option Prices (2005)
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Working Paper: Jacknifing Bond Option Prices (2002)
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