Jackknifing Bond Option Prices

By Peter C. B. Phillips, Jun Yu. 2005

130 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/4fb1ea398ab89a807863654b98408c66bde2a751

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Citations in the corpus

Bias in the estimation of the mean reversion parameter in continuous time models (2012, methodology): “In Phillips and Yu (2005) the jackknife method of Quenouille (1956) was suggested to reduce the bias.”
Folklore Theorems, Implicit Maps, and Indirect Inference (2012, background): “This bias is particularly important because of its implications for derivative pricing in finance (Phillips and Yu, 2005; 2009).”
Simulation-Based Estimation of Contingent-Claims Prices (2009, unknown): “samples as shown recently in Phillips and Yu (2005) ; and when biased estimated parameters”
Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance (2007, methodology): “The problem of estimation bias turns out to be of even greater importance in the practical use of econometric estimates in asset and option pricing, where there is nonlinear dependence of the pricing functional on the parameter estimates, as shown in Phillips and Yu (2005a).”
Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks (2013, unknown): “adopted by Ang, Piazzesi, and Wei (2003) and Bikbov and Chernov (2008), among others, they all imply the same theoretical bond prices and that the same risks are priced in the underlying economies.”
A jump diffusion model for VIX volatility options and futures (2010, methodology): “estimation requires large data sets (e.g., Phillips and Yu, 2005 ).”
Jackknife estimation of stationary autoregressive models (2013, unknown): “This expression corresponds to the form of jackknife estimator used by Phillips and Yu (2005).”
Term Structure Estimation with Survey Data on Interest Rate Forecasts (2005, methodology): “For example, options data might help, as suggested by Phillips and Yu (2005).”