Asymptotic Expansions for Market Risk Assessment: Evidence in Energy and Commodity Indices

The increasing volatility experienced in financial and commodity markets has motivated the search of frequency functions with more complex attributes to characterize their asset returns distribution. In this research, two semi-nonparametric distributions are proposed and compared, the Gram-Charlier expansion and a novel Edgeworth expansion for the Student’s t, to estimate the value-at-risk and the expected shortfall in four indices related to energy, metals, mining, and physical commodities. Backtesting performance is assessed in terms of Kupiec and Independence tests for value at risk and the recent proposal by Acerbi and Székely for the expected shortfall. Our results indicate that the Student’s t expansion density adequately fits the returns of different indices and exhibits the best performance for value at risk and expected shortfall backtesting. Consequently, the Student’s t expansion density, which encompasses the Gram-Charlier distribution as the degrees of freedom parameter tends to infinity, reveals as a flexible and accurate methodology for risk management purposes in energy and commodity markets.