Realized cumulants for martingales
Probability
2021-01-12 v2
Abstract
Generalizing the realized variance, the realized skewness (Neuberger, 2012) and the realized kurtosis (Bae and Lee, 2020), we construct realized cumulants with the so-called aggregation property. They are unbiased statistics of the cumulants of a martingale marginal based on sub-period increments of the martingale and its lower-order conditional cumulant processes. Our key finding is a relation between the aggregation property and the complete Bell polynomials. For an application we give an alternative proof and an extension of a cumulant recursion formula recently obtained by Lacoin et al. (2019) and Friz et al. (2020).
Keywords
Cite
@article{arxiv.2010.08293,
title = {Realized cumulants for martingales},
author = {Masaaki Fukasawa and Kazuki Matsushita},
journal= {arXiv preprint arXiv:2010.08293},
year = {2021}
}