Kullback-Leibler cluster entropy to quantify volatility correlation and risk diversity

Abstract

The Kullback-Leibler cluster entropy 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 D_C[P \| Q] provides complementary perspectives about the stochastic volatility process compared to the Shannon functional S_C[P]. While D_C[P \| Q] is maximum at the short time scales, 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.

Tasks

Reproductions