From Discrete to Continuous: Garch Volatility Modeling of the Bitcoin

The aim of the study is to determine the most appropriate discrete model for the volatility of Bitcoin returns using the discrete-time GARCH model and its extensions and compare it with the Levy-driven continuous-time GARCH model. For this purpose, the volatility of Bitcoin returns is modeled using daily data of the Bitcoin / United States Dollar exchange rate. By comparing discrete-time models according to information criteria and likelihood values, the All-GARCH model with Johnson's-SU innovations is found as the most adequate model. The persistence of the volatility and half-life of the volatility of the returns are calculated according to the estimation of the discrete model.This discrete model has been compared with the continuous model in which the Levy increments are derived from the compound Poisson process using various error measurements. In conclusion, it is found that the continuous-time GARCH model shows a better performance in predicting volatility.