Dynamic selection of Gram-Charlier expansions with risk targets: an application to cryptocurrencies

【Author】 Jimenez, Ines; Mora-Valencia, Andres; Perote, Javier

【Source】RISK MANAGEMENT-AN INTERNATIONAL JOURNAL

【影响因子】2.560

【Abstract】This paper implements a procedure for dynamically selecting the Gram-Charlier approximation that best fits the empirical distribution of cryptocurrency returns at any point in time. The endogenous selection of the Gram-Charlier expansion length exploits its property for approximating frequency distributions through a flexible number of parameters that allows capturing changes at the tails provoked by new extreme events. The procedure is based on the differences between the cumulative distribution function of Gram-Charlier distributions with a particular focus on the fitting of the distribution left tail for risk assessment purposes. The method is tested through backtesting techniques for a group of major cryptocurrencies. The results show that the selection of the Gram-Charlier expansion order on the basis of cumulative distribution function dynamics, provides, in most cases, a significant improvement for conditional coverage compared to the use of fixed-order Gram-Charlier expansions. The method seems to be a useful tool for risk management purposes, especially for highly volatile assets such as cryptocurrencies.

【Keywords】Frequency functions; Gram-Charlier series; Cumulative distribution function; Backtesting; Cryptocurrencies

【发表时间】

【收录时间】2022-01-01

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