Polynomial adjusted Student-t densities for modeling asset returns

We present a polynomial expansion of the standardized Student-t distribution. Our density, obtained through adjusted method in Bagnato, Potí, and Zoia (2015. “The Role Orthogonal Polynomials Adjusting Hyperbolic Secant Logistic Distributions to Analyse Financial Asset Returns.” Statistical Papers 56 (4): 1205–12340), is an extension Gram–Charlier density Jondeau Rockinger (2001. “Gram-Charlier Densities.” Journal Economic Dynamics Control 25 (10): 1457–1483). derive closed-form expressions moments, distribution function skewness–kurtosis frontier for well-defined density. An empirical application also implemented modeling heavy-tailed skewed distributions daily asset returns. Both in-sample backtesting analysis show that this new can be good candidate risk management.