Analysing The Rate Of Volatility For Crypto Exchanges

Generalised Autoregressive Conditional Heteroskedasticity (GARCH) models can come in handy for predicting the rate of the volatility of traditional assets like stocks and bonds and their indices. This is why GARCH has been able to stick around since the 80s but when it comes to cryptocurrencies like Bitcoin, Ethereum and Litecoin, they yield incorrect estimates for Value at Risk and the Expected Shortfall.

The authors of a new paper confirm this for more than a thousand GARCH models fitted to the returns of exchange rates of each of the cryptocurrencies. Guglielmo Maria Caporale, Timur Zekokh are the authors of the new CESifo Working Paper which looks into several different approaches to the modelling of price volatility among digital currencies such as Bitcoin, Ethereum and so on.

The two authors start off the paper with the observation that standard GARCH models don’t work very well for this reason.

Markov Switching

The two authors find that by adding Markov switching to the GARCH models will make them significantly more reliable.

For those that don’t know, Markov Switching has been around almost as long as GARCH has. Stata describes Markov Switching as “being abrupt; the probability instantly changed. Such Markov models are called dynamic models. Markov models can also accommodate smoother changes by modeling the transition probabilities as an autoregressive process. Thus switching can be smooth or abrupt.” The key paper is a 1989 article by J.D Hamilton in Econometrica, “a new approach to the economic analysis of nonstationary time series and the business cycle.”

The new approach Hamilton’s involved simply recognised regime changes. As reported by AllAboutAlpha, by using this approach to modelling will typically invoke just two different regimes, one for negative growth rate and the other for positive. “Thus, when an economy in recession has hit bottom and begins recovery, we speak of a Markov switch between regimes, and when a growing economy hits its peak and heads down … another switch.”

It is worth it to build the switch into the models because as the two authors observe “standard GARCH models can produce biased results if the series display structural breaks.”

What’s new?

What’s new to the paper is the finding that two regime models do outperform in reference to the volume of the exchange rates in Bitcoin, Ethereum, Ripple and Litecoin.

In order to test this, Caporale and Zekokh use the Model Confidence Set procedure as explained by PS Hansen in an article in Econometrica at the turn of the decade.

What are your thoughts? Let us know what you think down below in the comments!