A new methodology is proposed to estimate theoretical prices of financial contingent claims whose values are dependent on some other underlying financial assets. In the literature, the preferred choice of estimator is usually maximum likelihood (ML). ML has strong asymptotic justification but is not necessarily the best method in finite samples. This paper proposes a simulation-based method. When it is used in connection with ML, it can improve the finite-sample performance of the ML estimator while maintaining its good asymptotic properties. The method is implemented and evaluated here in the Black-Scholes option pricing model and in the Vasicek bond and bond option pricing model. It is especially favored when the bias in ML is large due to strong persistence in the data or strong nonlinearity in pricing functions. Monte Carlo studies show that the proposed procedures achieve bias reductions over ML estimation in pricing contingent claims when ML is biased. The bias reductions are sometimes accompanied by reductions in variance. Empirical applications to U.S. Treasury bills highlight the differences between the bond prices implied by the simulation-based approach and those delivered by ML. Some consequences for the statistical testing of contingent-claim pricing models are discussed.

Prices of interest rate derivative securities depend crucially on the mean reversion parameters of the underlying diffusions. These parameters are subject to estimation bias when standard methods are used. The estimation bias can be substantial even in very large samples and much more serious than the discretization bias, and it translates into a bias in pricing bond options and other derivative securities that is important in practical work. This article proposes a very general and computationally inexpensive method of bias reduction that is based on Quenouille's (1956; Biometrika, 43, 353–360) jackknife. We show how the method can be applied directly to the options price itself as well as the coefficients in the models. We investigate its performance in a Monte Carlo study. Empirical applications to U.S. dollar swap rates highlight 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.