Formulating MCoVaR to quantify joint transmissions of systemic risk across crypto and non-crypto markets : a multivariate copula approach

Evidence that cryptocurrencies exhibit speculative bubble behavior is well documented. This evidence could trigger global financial instability leading to systemic risk. It is therefore crucial to quantify systemic risk and investigate its transmission mechanism across crypto markets and other global financial markets. We can accomplish this using the so-called multivariate conditional value-at-risk (MCoVaR), which measures the tail risk of a targeted asset from each market conditional on a set of multiple assets being jointly in distress and on a set of the remaining assets being jointly in their median states. In this paper, we aimed to find its analytic formulas by considering multivariate copulas, which allow for the separation of margins and dependence structures in modeling the returns of the aforementioned assets. Compared to multivariate normal and Student's t benchmark models and a multivariate Johnson's SU model, the copula-based models with non-normal margins produced a MCoVaR forecast with superior conditional coverage and backtesting performances. Using a corresponding Delta MCoVaR, we found the crypto assets to be potential sources of systemic risk jointly transmitted within the crypto markets and towards the S&P 500, oil, and gold, which was more apparent during the COVID-19 period encompassing the recent 2021 crypto bubble event.