Kullback-Leibler cluster entropy to quantify volatility correlation and risk diversity
Kullback-Leibler cluster entropy to quantify volatility correlation and risk diversity ArXiv ID: 2409.10543 “View on arXiv” Authors: Unknown Abstract The Kullback-Leibler cluster entropy $\mathcal{“D_{C”}}[“P | Q”] $ is evaluated for the empirical and model probability distributions $P$ and $Q$ of the clusters formed in the realized volatility time series of five assets (SP&500, NASDAQ, DJIA, DAX, FTSEMIB). The Kullback-Leibler functional $\mathcal{“D_{C”}}[“P | Q”] $ provides complementary perspectives about the stochastic volatility process compared to the Shannon functional $\mathcal{“S_{C”}}[“P”]$. While $\mathcal{“D_{C”}}[“P | Q”] $ is maximum at the short time scales, $\mathcal{“S_{C”}}[“P”]$ is maximum at the large time scales leading to complementary optimization criteria tracing back respectively to the maximum and minimum relative entropy evolution principles. The realized volatility is modelled as a time-dependent fractional stochastic process characterized by power-law decaying distributions with positive correlation ($H>1/2$). As a case study, a multiperiod portfolio built on diversity indexes derived from the Kullback-Leibler entropy measure of the realized volatility. The portfolio is robust and exhibits better performances over the horizon periods. A comparison with the portfolio built either according to the uniform distribution or in the framework of the Markowitz theory is also reported. ...