A Weighted Integration of GARCH and IV-based VaR for
Crypto Markets
Abstract
Previous literature has shown that, using over 20 years of daily data from the S&P 500, Dow Jones
Industrial Average, and Nasdaq 100 indices, VaR models based on implied volatility are generally
outperformed by those using a simple GJR-GARCH historical volatility model. The study underscores
that forecasting volatility and predicting a quantile of the return distribution are distinct objectives.
While implied volatility is effective for the former, it is less suitable for the latter due to the complex,
non-linear dynamics of the volatility risk premium.
We aim to replicate the analysis cited above in the Bitcoin market - characterized by a typically-high
volatility with jumps in price - and to ensemble a model that results in a weighted average of the
GARCH-VaR and the IV-VaR, where weights are computed with a numerical procedure.
Research Project
The Bitcoin market, a rapidly expanding financial ecosystem, has gained substantial attention due to
its high volatility and increasing institutional interests. As more and more investors enter the market,
Risk management tools becomes critical in a scenario where investors and firms are involved to
invest in this risky market.. In this study, we aim to replicate the analysis of traditional markets
conducted in the paper by Bams, Blanchard, and Lehnert (2017), which compared the performance of
Value at Risk (VaR) models based on implied volatility versus historical volatility derived from a
GJR-GARCH framework. We will apply this analysis to the Bitcoin market, comparing the
effectiveness of these two distinct approaches in forecasting VaR and exploring whether an ensemble
model can further improve risk forecasting accuracy.
Specifically, we will develop a model that combines the two contrasting approaches to volatility
forecasting. Using data on BTC price returns, we will compute the GARCH-VaR, and using BTC
options quotes, we will derive the implied volatility-based VaR (IV-VaR). These two risk measures will
then be combined into a weighted ensemble, where the weights are optimized by minimizing the
mean-squared error (MSE) between the ensemble VaR and the actual realized losses.
We perform a walk-forward backtest of the ensemble model on a test dataset of daily BTC returns
from January 2018 to August 2024. We report several VaR forecasts at the 10%, 5% and 1% levels.
We then compare our model’s forecasts with the GARCH-VaR forecasts using the Kupiec (1995) LR
test and the Engle and Manganelli (2004) dynamic quantile test, and an ad-hoc loss function for
relative forecast accuracy.
Both static and dynamic weights are used and the resulting models are compared in terms of VaR
efficiency against a simple GARCH-VaR specification. Our ultimate objective is to assess whether
combining these different approaches yields a more reliable VaR measure for a market as volatile and
unpredictable as Bitcoin.
References
Bams, D., Blanchard, G., & Lehnert, T. (2017). Volatility measures and Value-at-Risk. International
Journal of Forecasting, 33(4), 848–863.
Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional Autoregressive Value at Risk by
Regression Quantile. Journal of Business and Economic Statistics, 22, 367-381.