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.
Phillips, Peter C.B. and Yu, Jun, "Jackknifing Bond Option Prices" (2003). Cowles Foundation Discussion Papers. 1657.