Forecasting volatility and value-at-risk for cryptocurrency using GARCH-type models: the role of the probability distribution

ABSTRACT

This study investigates the role of the probability distribution in forecasting the volatility and value-at-risk (VaR) of cryptocurrency returns using generalized auto-regressive conditional heteroskedasticity (GARCH)-type models. We consider GARCH, EGARCH, GJR-GARCH, TGARCH and Realized GARCH models and show that the role of the probability distribution varies across different situations. A skewed and heavy-tailed distribution contributes to better performance in forecasting the VaR; however, it does not improve the accuracy of volatility forecasting. The results help us to better understand the role of the probability distribution in GARCH-type models.

KEYWORDS:

• Probability distribution
• cryptocurrency
• volatility
• value-at-risk
• Realized GARCH

JEL CLASSIFICATION:

• C52
• G16

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The original data can be downloaded from https://firstratedata.com/b/31/crypto-active.

Notes

¹ We obtain intraday data from https://firstratedata.com/b/31/crypto-active and employ a 5-min sampling frequency to estimate the realized kernel. The Oxford MFE Toolbox for MATLAB is used for this estimation.

² We fit an AR (1) model for the conditional mean.

³ We use variance as a measure of volatility.

⁴ The leverage functions are specified as $\delta \left(z_t\right)={\delta }_1{z}_t+{\delta }_2\left(\left|z_t\right|-E\left(\left|z_t\right|\right)\right)$ and $\tau \left(z_t\right)={\tau }_1{z}_t+{\tau }_2\left(\left|z_t\right|-E\left(\left|z_t\right|\right)\right)$.

⁵ We can evaluate VaR models using this loss function because VaR is elicitable.