Analysis of leverage and inverse asymmetry effects in cryptocurrency volatility with autoregressive conditional heteroskedasticity models

Determining the volatility structures of cryptocurrencies, which are designed as decentralised payment instruments but are used as investment instruments due to their price fluctuations, is important for option pricing, portfolio diversification and risk assessment. The aim of this study is to determine the best volatility model for Bitcoin, Ethereum, BNB, Solana, Ripple, Cardano, Dogecoin, Polygon, Polkadot and Litecoin, which have the largest market capitalisation, and to question the existence of leverage and inverse asymmetry relationships in cryptocurrency volatilities. Due to different time periods, different methodologies, applications to different cryptocurrencies, high volatility of cryptocurrencies and changes in volatility structure, it can be said that there is no single best model for cryptocurrencies. The study uses ARCH, GARCH, EGARCH, TARCH, FIGARCH and FIEGARCH models, which are autoregressive conditional variance models, to determine the best model that reveals the volatility structures of cryptocurrencies. As a result, the best model for Bitcoin, BNB, Ethereum, Litecoin and Polygon is EGARCH (1 1), for Cardano and Polkadot GARCH (1 1), for Solana TARCH (1 1), for Dogecoin and Ripple FIGARCH (1 d 1). It also revealed the existence of leverage for Bitcoin, BNB, Ethereum, Dogecoin and Ripple, and inverse asymmetry for Litecoin, Polygon and Solana. There is no asymmetry for Cardano and Polkadot volatilities. Shock persistence is found to be short term for Solana, medium term for Bitcoin, Cardano, Ethereum and Litecoin, long term for BNB, Polkadot and Polygon, and long memory for Dogecoin and Ripple.