Simulation-based Estimation of Contingent-claims Prices
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. The present paper proposes instead a simulation-based method that improves the ﬁnite sample performance of the ML estimator while maintaining its good asymptotic properties. The methods are implemented and evaluated here in the Black-Scholes option pricing model and in the Vasicek bond pricing model, but have wider applicability. Monte Carlo studies show that the proposed procedures achieve bias reductions over ML estimation in pricing contingent claims. The bias reductions are sometimes accompanied by reductions in variance, leading to signiﬁcant overall gains in mean squared estimation error. Empirical applications to US 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.