Bitcoin Asymmetric Volatility Estimation: Improving GARCH Forecasts

Asymmetric Volatility

Bitcoin is known for having a fat tailed return distribution and likewise volatility. GARCH is a model that we can use to estimate and forecast volatility, but there are other models that account for factors that GARCH does not. For instance, the GARCH model, which we built previous here , uses a long term average of volatility parameter (which is good in general!). But the model weights shocks to both the upside and the downside the same (symmetric). However, we know that in financial markets, negative shocks to price are almost always more volatile than upside squeezes. In this article, we will create a Bitcoin (BTC) model that adds an extra parameter for downside volatility. This in effect, will add a penalty into model for downside shocks, which we hope will improve forecasts.

GJR-GARCH Model Information

According to published research, the GJR-GARCH model will generally perform better than the GARCH model. In effect, GJR is GARCH, but with an extra parameter (for downside shocks). Therefore, in theory, it should fit the data just as good as GARCH, and with a slight improvement. GJR-GARCH was published by Glosten, Jagannathan, and Runkle in 1993, and is now somewhat referred to as a "core" model. There are numerous other assymmetric models to account for other parameters worth mentioning: EGARCH, APARCH, TARCH, TS-GARCH, and NARCH. In order to compare which model performs better, rank the corresponding AIC scores.

Python Implementation

We will still leverage the ARCH library that we previously used in the GARCH Plus+ code; and modify the parameters. As always, our code is fully commented for your benefit to modify, use or understand. More documentation concerning the arch library can be found here.