Volatility Forecasting with GARCH Models

Abstract

We conduct a systematic study on the statistical properties of returns of the two major cryptocurrencies, Bitcoin and Ether. We show that most stylized facts found for other financial returns are also exhibited in BTC and ETH returns. The returns of BTC and ETH are fat-tailed with little or no correlations in returns themselves but significant autocorrelations in absolute and squared returns. The volatilities are clustered together with asymmetric impact from positive or negative returns. We further estimate six popular GARCH models for the BTC and ETH return series and find that the two-component GJR model has the best fit overall. The out-sample forecasting exercise shows that the two-component GJR model does a better job of predicting future volatility than either realized volatility or implied volatility. 

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Introduction

In this paper, we conduct a systematic study on the statistical properties of the returns of the two major cryptocurrencies, Bitcoin (BTC) and Ether (ETH), and further build statistical models for forecasting their volatilities.  We then compare the effectiveness of our volatility forecasting vs. using implied volatility and realized volatility as forecasting tools.  Studies of other financial time series data have found at least the following stylized facts which seem to be common to a wide variety of markets and instruments (see Cont 2001):  

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1. Fat tails: the (unconditional) distribution of returns seems to exhibit large leptokurtosis. This represents a greater likelihood of extreme returns occurring than what is implied by a normal distribution.
2. Volatility clustering: different measures of volatility display a positive autocorrelation over several days, which quantifies the fact that high-volatility events tend to cluster.
3. Absence of autocorrelations: (linear) autocorrelations of asset returns are often insignificant, except for very small intraday time scales for which microstructure effects come into play.
4. Slow decay of autocorrelation in absolute or squared returns: the autocorrelation function of absolute returns decays slowly as a function of the time lag, roughly as a power law with an exponent b∈[0.2,0.4] . This is sometimes interpreted as a sign of long-range dependence.
5. Leverage effect: most measures of volatility of an asset are negatively correlated with the returns of that asset. 

It will be interesting to see if the above “stylized facts” are also exhibited in cryptocurrency returns. This will shed light on the form of the statistical model we should use in predicting cryptocurrency volatility. Section 2 presents the result of such a study for BTC and ETH. We show that like other speculative returns, cryptocurrency returns also exhibit most of the stylized facts listed above. Further details can be found in Gosal, McMurran and Ding (2022). Section 3 estimates the six most commonly used GARCH models for BTC and ETH. The results show that the two-component GARCH models capture the long-term volatility persistence (aka long memory) and short run volatility dynamics quite well. Section 4 compares the results of volatility forecasting using the six aforementioned GARCH models with the realized and implied volatilities. Based on the commonly used Bias-stat and Q-stat, the GARCH models are proven to produce superior volatility forecasts relative to using realized volatility or implied volatility. Section 5 concludes the paper.