%L discovery10189728 %T On some semi-parametric estimates for European option prices %D 2024 %O Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work. %A Carlo Marinelli %J Journal of Applied Probability %X We show that an estimate by de la Peña, Ibragimov, and Jordan for E(X − c)âº, with c a constant and X a random variable of which the mean, the variance, and P(X ⪬ c) are known, implies an estimate by Scarf on the infimum of E(X ∧ c) over the set of positive random variables X with fixed mean and variance. This also shows, as a consequence, that the former estimate implies an estimate by Lo on European option prices. %I Applied Probability Trust %K Probabilistic inequalities; bounds for option prices;