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1 results

On some semi-parametric estimates for European option prices
Part of
- Mathematical finance
- Distribution theory - Probability
Carlo Marinelli
Journal:

Journal of Applied Probability / Volume 61 / Issue 3 / September 2024

Published online by Cambridge University Press:

14 February 2024, pp. 999-1009

Print publication:

September 2024
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We show that an estimate by de la Peña, Ibragimov, and Jordan for ${\mathbb{E}}(X-c)^+$, with c a constant and X a random variable of which the mean, the variance, and $\mathbb{P}(X \leqslant c)$ 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.