Mudança de regime markoviano na dinâmica de volatilidade do mercado de criptomoedas e seus reflexos na previsão do value-at-risk

Abstract

This research proposes a comparative analysis of some conditional volatility models for the calculation of Value-at-Risk (VaR) applied to the main financial series of the crypto-currencies market. Conditional volatility models of the ARCH family were used, taking into account markov-switching changes. Specifically, we used the EGARCH and MS-EGARCH models estimated from four different distributions, Normal, Normal Asymmetric, Student-t and Student-t Asymmetric, to model and make predictions for the time series of Bitcoin, Bitcoin Cash, Ripple, Ethereum, EOS and Stellar. Estimates confirm the existence of two states: the first regime is characterized greater volatility and less affected by asymmetries, while the second reveals greater effect of the arrival of information, ie is more sensitive to asymmetric shock and less persistence of volatility. To complement the analysis of the volatility models, risk estimates were generated from Value-at-Risk. Thus, we performed the process to obtain the estimates of the VaR estimates for 100 steps forward with readjustment of the parameters at each step obtained for α = 1% and α = 5%. It should be noted that MS-EGARCH exceeded EGARCH-type models by 1%, indicating that this model is the most appropriate for estimation of the value at risk in the extreme quantile of 1%, that is, the model with change of Markovian regime made a prediction closer to perfection. However, in 5% the occurrence of losses was similar between the models. In this case, regardless of the number of regimes, there was an overestimation of VaR, that is, there were violations between expected and expected losses. As there were no statistically robust results, there is no way to imply that the MS-EGARCH model exceeds in large magnitudes the EGARCH model in a single prediction of 100 steps forward. Instead, it can be inferred that models with regime change can more accurately accommodate the properties of the financial returns and dynamics present in their volatility.