Comparison of Fuzzy Risk Forecast Intervals for Cryptocurrencies

Data-driven volatility models and neuro-volatility models have the potential to revolutionize the area of Computational Finance. Volatility measures the variation of a time series data, and thus it is also a driving factor for the risk forecasting of returns from investment in cryptocurrencies. A cryptocurrency is a decentralized medium of exchange that relies on cryptographic primitives to facilitate the trustless transfer of value between different parties. Instead of being physical money, cryptocurrency payments exist purely as digital entries on an online ledger called blockchain that describe specific transactions.Many commonly used risk forecasting models do not take into account the uncertainty associated with the volatility of an underlying asset to obtain the risk forecasts. Some tools from the fuzzy set theory can be incorporated into the forecasting models to account for this uncertainty. Interest in the use of hybrid models for fuzzy volatility forecasts is growing. However, a major drawback is that the fuzzy coefficient hybrid models used in fuzzy volatility forecasts are not data-driven. This paper uses fuzzy set theory with data-driven volatility and data-driven neuro-volatility forecasts to study the fuzzy risk forecasts. The study focuses on long-term volatility forecasts with daily price data while briefly exploring forecasting models with high-frequency (hourly) data as an avenue for future research. Simple yet effective models incorporating fuzziness to obtain fuzzy risk volatility forecasts and fuzzy VaR forecasts are presented. The key underlying idea, unlike the existing risk forecasting, is the use of a hybrid nonlinear adaptive fuzzy model for volatility.