Impact of bias in the estimation of American-style options by Monte Carlo simulation

Purpose The purpose of this paper is to investigate the impact of bias error resulted from using Monte Carlo simulation in evaluating the American-style option value. Design/methodology/approach The authors develop an analytical approximation formula to quantify the bias error under the assumption of conditionally independent and identically distributed samples of asset prices. The bias arises from the nested optimization and expectation calculation. The formula is then used to numerically quantify the bias and as an objective function for bias minimization for a given budget of samples. Findings Monte Carlo methods used in valuation of American-style options can results in bias error ranging from 2 to 10 per cent of the option value. The bias error can be reduced up to 50 per cent either by performing a better scheme for sampling or by efficiently allocating sample size. Research limitations/implications The running time of the proposed procedure can be improved by using a specialized algorithm to solve the sample size allocation problem instead of using a commercially available subroutine MINOS. Other sampling procedures for bias reduction may be extended and applied to this multi-stage problem. Practical implications The methodology can help to more accurately approximate the option value. Originality/value The paper provides a method to develop an analytical approximation for bias error and provide a numerical experiment to test the methodology.