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On some semi-parametric estimates for European option prices

Part of: Mathematical finance Distribution theory - Probability

Published online by Cambridge University Press:  14 February 2024

Carlo Marinelli Open the ORCID record for Carlo Marinelli [Opens in a new window]
Carlo Marinelli*
Affiliation:
University College London
*
*Postal address: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK. Email: c.marinelli@ucl.ac.uk
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Abstract

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.

Keywords

Probabilistic inequalitiesbounds for option prices

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 91G20: Derivative securities 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 11
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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References

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