On some semi-parametric estimates for European option prices

Carlo Marinelli

Papers from arXiv.org

Abstract: We show that an estimate by de la Pe\~na, Ibragimov and Jordan for $\mathbb{E}(X-c)^+$, with $c$ a constant and $X$ a random variable of which the mean, the variance, and $\mathbb{P}(X \leq c)$ are known, implies an estimate by Scarf on the infimum of $\mathbb{E}(X \wedge c)$ 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.

Date: 2023-06
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Published in J. Appl. Probab. 61 (2024) 999-1009

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