On some semi-parametric estimates for European option prices
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 $\mathbb{P}(X \leq c)$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2023
- DOI:
- 10.48550/arXiv.2306.10929
- arXiv:
- arXiv:2306.10929
- Bibcode:
- 2023arXiv230610929M
- Keywords:
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- Mathematics - Probability;
- Quantitative Finance - Pricing of Securities
- E-Print:
- 10 pages