Modeling the Volatility of Crypto Exchange Rates

Modeling the Volatility of Crypto Exchange Rates

GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models are very useful for estimating the volatility for a lot of more traditional assets (stocks and bonds) and their indices, which is why they’ve been around since the 1980s. But when they’re used for Bitcoin, Ethereum, Ripple, and Litecoin they yield incorrect predictions for Value at Risk and Expected Shortfall.

Authors of a new paper confirm this for more than a thousand GARCH models fitted to the log returns of the exchange rates of each of those currencies. The new CESifo* working paper looks at various approaches to the modeling of price volatility among the cryptocurrencies.

Authors Guglielmo Maria Caporale of Brunel University London, and Timur Zekokh of National Research University, Moscow, begin with the observation that standard GARCH models don’t work very well for this purpose.

Markov Switching

What to do then? The authors find that adding Markov-switching to the GARCH models makes them considerably more reliable.

Markov switching (otherwise known as Markov transition modeling), is named for the Russian mathematician Andrey Markov, and has been around almost as long as GARCH. The key paper (in the development of the former) 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.”

Hamilton’s “new approach” involved simply recognizing regime changes. Typically, though not inevitably, using this approach to modeling invokes just two different “regimes,” one for a positive and the other for a negative growth rate. 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 valuable to build the switch into the models because, as Caporale and Zekokh observe, “standard GARCH models can produce biased results if the series display structural breaks.”

So, what happens when such shifts are built into the GARCH models? Caporale and Zekokh are not the first to attempt this. As they acknowledge, regime shifts have long been applied to the GARCH models of commodity price volatility, exchange rate returns, etc. These “two-regime” models outperform the traditional or “one-regime” models for some times series, but not for others.

What is New

What is new in the paper is the finding that two regime models do outperform in regard to the vol of the exchange rates in above-named cryptocurrencies.

For testing this, Caporale and Zekokh use the Model Confidence Set (MDS) procedure as explained by P.S. Hansen et al. in an article in Econometrica at the start of this decade.

They look both to VaR and to ES under the influence of the extreme value theory that became important around the turn of the millennium. EVT says that VaR can be misleading insofar as tails can be “fat,” swans can be “black,” etc. So, a model should be tested not only against what is usually the case, but against what unusual events can be expected. The Basel Committee has recently made the transition from VaR to ES as its main market risk metric, in terms of the minimum capital requirements for banks. Caporale and Zekokh don’t go quite that far. They treat VaR and ES as partners rather than replacing the former altogether with the latter.

The New Improved Model

The resulting MS [Markov switching] GARCH model will, they believe, be of value to investors who are considering or who already have cryptos in their portfolio, and it will be of value to the Securities and Exchange Commission, as to the regulators in other nation-states which have under consideration the oversight of crypto exchanges.

With regard to further research, Caporale and Zekokh suggest that intraday data could be employed to fine tune the testing of models, and that multivariate GARCH models could help look into the linkages among the various cryptos, for example between Altcoin and Bitcoin.

*CESifo is part of the Center for Economic Studies, which is itself an independent institute within the University of Munich.

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