This paper studies a large number of Bitcoin options traded on the options exchange Deribit. We use the trades to calculate implied volatility and analyze if volatility forecasts can be improved using such information. Implied volatility is less accurate than ARMA or HAR model forecasts in...

There is a well documented asymmetric return - volatility effect of equity returns, that is, negative shocks increase volatility by more than positive shocks. This paper analyzes the return - volatility relationship of commodity price changes and finds an inverted asymmetric effect with a...

This article analyzes asymmetric volatility effects for the 20 largest cryptocurrencies and reports a very different asymmetry compared to equity markets: positive shocks increase the volatility by more than negative shocks. We explain this atypical effect for financial assets with trading...

This paper analyzes high-frequency estimates of good and bad realized volatility of Bitcoin. We show that volatility asymmetry depends on the volatility regime and the forecast horizon. For one-day ahead forecasts, good volatility commands a stronger impact on future volatility than bad...

Existing multivariate GARCH models either impose strong restrictions on the parameters or do not guarantee a well-defined (positive definite) covariance matrix. I discuss all main Multivariate GARCH models and focus on the BEKK model for which it is shown that the covariance and correlation is...