Estimating Parametric Models of Probability Distributions

摘要

Noting that risk neutral distributions are estimated by minimizing the squared deviations between market and model option prices we consider using option payoff moments in estimating distributional parameters from a sample of observations. It is observed, in particular when compared to maximum likelihood estimation, that digital option payoff moments yield the lowest chisquare statistics for a test of uniformity for data transformed to the unit interval by the estimated distribution function.