نوع مقاله : علمی - پژوهشی
عنوان مقاله English
نویسندگان English
Abstract
Objective: Cryptocurrency returns exhibit heavy tails, strong volatility clustering, and sudden, asymmetric jumps and crashes, making tail risk difficult to measure in this market. Value at Risk (VaR) indicates only the loss threshold that is exceeded with a given probability, whereas Expected Shortfall (ES) also quantifies the magnitude of losses beyond that threshold. Because ES can be evaluated only jointly with VaR, the two are best forecast together. This study evaluates and compares the performance of the semiparametric CAViaR–CARE model, in which VaR and ES are estimated jointly using the asymmetric Laplace distribution, in the cryptocurrency market. The central question is whether combining CAViaR dynamics for VaR with a CARE structure for ES can provide a competitive and credible framework for measuring tail risk in a market marked by extreme volatility, heavy tails, and volatility clustering.
Method: The data consist of daily returns on six selected cryptocurrencies (Bitcoin, Ethereum, Ripple, Litecoin, Binance Coin, and Cardano) from early January 2018 to early January 2026, yielding 2,925 observations per asset. VaR follows an asymmetric-slope CAViaR process that responds separately to positive and negative returns. ES follows its own autoregressive path, and all parameters are estimated in one step by maximizing the asymmetric Laplace quasi-likelihood. Using a 1,825-day rolling window, we produce 1,100 one-day-ahead forecasts at the 1% and 5% risk levels and compare them with historical simulation (HS), filtered historical simulation (FHS), GARCH-t, GJR-GARCH, GARCH-EVT and the model of Taylor (2019). The Kupiec, Christoffersen, dynamic quantile, and McNeil–Frey backtests assess forecast adequacy; the asymmetric Laplace (AL), Fissler–Ziegel (FZ), and Acerbi–Szekely (AS) scoring functions rank the models; and the Diebold–Mariano (DM) test and the model confidence set (MCS) identify which differences are statistically reliable. We also separately examine how the length of the estimation window, ranging from 1,100 to 2,200 days, affects the results.
Findings: The descriptive statistics show high volatility, heavy tails, and asymmetric behavior in the returns of all six cryptocurrencies, indicating the need for dynamic, tail-focused models in this market. In the backtests, CAViaR–CARE is the only model that passes the Kupiec test across all twelve asset–risk level combinations. Its violation rate lies between 1.00% and 1.55% at the 1% level and between 4.82% and 5.55% at the 5% level. It passes 28 of 30 backtests at the 1% level and 29 of 30 at the 5% level. By contrast, the GARCH-type models, FHS, and HS are clearly too conservative at the 5% level. CAViaR–CARE also has the lowest average loss under all three scoring functions and, like Taylor's model, remains in the MCS for every asset and every criterion, while HS drops out of the set in 19 of 36 cases. That said, most of its differences from FHS, GARCH-EVT, and Taylor's model at the 1% level are not statistically significant, although no competitor is significantly better in any of the 216 DM comparisons. When the window length changes, its violation rate stays between 1.26% and 1.40% at the 1% level and between 5.01% and 5.17% at the 5% level, and it stays in the MCS in 143 of 144 cases, but its first place in the rankings does not survive every window length.
Conclusion: The results suggest that CAViaR–CARE can serve as a dynamic, semiparametric, and credible framework for jointly forecasting VaR and ES in cryptocurrency markets. However, no model examined is uniformly superior across all assets and tests; performance varies by asset, risk level, and evaluation criterion. Its main strength is stable coverage close to the nominal level, which matters when VaR is used to set margins or trading limits, because an overly conservative model ties up more capital than needed. For practitioners, the message is that backtesting should be combined with joint, consistent scoring functions, and that the best-performing models, when they are statistically indistinguishable, are better used together as a set than replaced by a single “winner.”
کلیدواژهها English
