ISSN 0253-2778

CN 34-1054/N

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Cryptocurrency risk measurement based on MIDAS-Expectile regression model

  • 1.

    School of Management, University of Science and Technology of China, Hefei 230026, China

  • 2.

    International Institute of Finance, University of Science and Technology of China, Hefei 230601,China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.06.020
  • Received Date: 09 April 2020
  • Accepted Date: 20 May 2020
  • Rev Recd Date: 20 May 2020
  • Publish Date: 30 June 2020
    Abstract

  • Abstract

    As an alternative to the quantile-based QVaR, the risk measure EVaR based on the Expectile model is simpler to calculate and can more accurately reflect the effects of extreme values. In order to make full use of the information contained in mixed frequency data, a MIDAS-Expectile regression model was constructed, and the estimation of the parameters and conditional EVaR were obtained based on the nonlinear asymmetric least squares method. The asymptotic normality of the estimates and coverage test for conditional Expectile were also given. In addition, the likelihood function and information criterion of the Expectile regression model were given from the perspective of maximum likelihood estimation, which could compare and test different models. In order to study the financial risks of cryptocurrencies, in the empirical part, the MIDAS-Expectile regression model was applied to the measurement of cryptocurrency returns risk, and the risk contagion of other tradition financial markets to this emerging financial asset was discussed. The empirical results of the risk of cryptocurrency monthly data indicate that signals from other financial markets will have a significant or positive or negative impact on the risks of the cryptocurrency market, and that the cryptocurrency market is not isolated from traditional financial markets.

    Abstract

    As an alternative to the quantile-based QVaR, the risk measure EVaR based on the Expectile model is simpler to calculate and can more accurately reflect the effects of extreme values. In order to make full use of the information contained in mixed frequency data, a MIDAS-Expectile regression model was constructed, and the estimation of the parameters and conditional EVaR were obtained based on the nonlinear asymmetric least squares method. The asymptotic normality of the estimates and coverage test for conditional Expectile were also given. In addition, the likelihood function and information criterion of the Expectile regression model were given from the perspective of maximum likelihood estimation, which could compare and test different models. In order to study the financial risks of cryptocurrencies, in the empirical part, the MIDAS-Expectile regression model was applied to the measurement of cryptocurrency returns risk, and the risk contagion of other tradition financial markets to this emerging financial asset was discussed. The empirical results of the risk of cryptocurrency monthly data indicate that signals from other financial markets will have a significant or positive or negative impact on the risks of the cryptocurrency market, and that the cryptocurrency market is not isolated from traditional financial markets.
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    • References(34)
  • [1]
    NEWEY W K, POWELL J L. Asymmetric least squares estimation and testing[J]. Econometrica: Journal of the Econometric Society, 1987, 55(4): 819-847.
    [2]
    KUAN C M, YEH J H, HSU Y C. Assessing value at risk with CARE, the conditional autoregressive expectile models[J]. Journal of Econometrics, 2009, 150(2): 261-270.
    [3]
    谢尚宇, 姚宏伟, 周勇. 基于 ARCH-Expectile 方法的 VaR 和 ES 尾部风险测量[J]. 中国管理科学, 2014, 22(9): 1-9.
    [4]
    XIE S, ZHOU Y, WAN A T K. A varying-coefficient expectile model for estimating value at risk[J]. Journal of Business & Economic Statistics, 2014, 32(4): 576-592.
    [5]
    KIM M, LEE S. Nonlinear expectile regression with application to value-at-risk and expected shortfall estimation[J]. Computational Statistics & Data Analysis, 2016, 94: 1-19.
    [6]
    谭常春, 操毅文, 叶五一. 基于 Expectile-based VaR 变点检测的金融传染分析[J]. 数理统计与管理, 2018, 37(2): 371-380.
    [7]
    DAOUIA A, GIRARD S, STUPFLER G. Extreme M-quantiles as risk measures: From L to Lp optimization[J]. Bernoulli, 2019, 25(1): 264-309.
    [8]
    许启发, 丁晓涵, 蒋翠侠. 基于 Expectile 回归的均值-ES组合投资决策[J]. 中国管理科学, 2018, 26(10): 20-29.
    [9]
    GHYSELS E, SANTA-CLARA P, VALKANOV R. The MIDAS touch: Mixed data sampling regression models[R]. CIRANO, 2004: 2004s-20.
    [10]
    GHYSELS E, SANTA-CLARA P, VALKANOV R. There is a risk-return trade-off after all[J]. Journal of Financial Economics, 2005, 76(3): 509-548.
    [11]
    MERTON R C. An intertemporal capital asset pricing model[J]. Econometrica, 1973, 41(5): 867-887.
    [12]
    GHYSELS E, SANTA-CLARA P, VALKANOV R. Predicting volatility: Getting the most out of return data sampled at different frequencies[J]. Journal of Econometrics, 2006, 131(1-2): 59-95.
    [13]
    GHYSELS E, PLAZZI A, VALKANOV R. Why invest in emerging markets? The role of conditional return asymmetry[J]. The Journal of Finance, 2016, 71(5): 2145-2192.
    [14]
    PETTENUZZO D, TIMMERMANN A, VALKANOV R. A MIDAS approach to modeling first and second moment dynamics[J]. Journal of Econometrics, 2016, 193(2): 315-334.
    [15]
    ANDREOU E. On the use of high frequency measures of volatility in MIDAS regressions[J]. Journal of Econometrics, 2016, 193(2): 367-389.
    [16]
    夏婷, 闻岳春. 经济不确定性是股市波动的因子吗?——基于 GARCH-MIDAS 模型的分析[J]. 中国管理科学, 2018, 26(12): 1-11.
    [17]
    尚玉皇, 郑挺国.短期利率波动测度与预测: 基于混频宏观-短期利率模型[J]. 金融研究, 2016(11): 47-62.
    [18]
    XU Q, WANG L, JIANG C, et al. A novel UMIDAS-SVQR model with mixed frequency investor sentiment for predicting stock market volatility[J]. Expert Systems with Applications, 2019, 132: 12-27.
    [19]
    AIGNER D J, AMEMIYA T, POIRIER D J. On the estimation of production frontiers: Maximum likelihood estimation of the parameters of a discontinuous density function[J]. International Economic Review, 1976,17(2): 377-396.
    [20]
    谢平, 石午光. 数字加密货币研究: 一个文献综述[J]. 金融研究, 2015(1): 1-15.
    [21]
    BUCHHOLZ M, DELANEY J, WARREN J, et al. Bits and bets, information, price volatility, and demand for Bitcoin[J]. Economics, 2012, 312: 2-48.
    [22]
    VAN WIJK D. What can be expected from the BitCoin[R]. Rotterdam, Netherlands: Erasmus Universiteit Rotterdam, 2013.
    [23]
    KRISTOUFEK L. What are the main drivers of the Bitcoin price? Evidence from wavelet coherence analysis[J]. PLoS ONE, 2015, 10(4): e0123923.
    [24]
    WALTHER T, KLEIN T. Exogenous drivers of cryptocurrency volatility: A mixed data sampling approach to forecasting[R]. St. Gallen, Switzerland: University of St. Gallen, 2018.
    [25]
    FRY J, CHEAH E T. Negative bubbles and shocks in cryptocurrency markets[J]. International Review of Financial Analysis, 2016, 47: 343-352.
    [26]
    URQUHART A, ZHANG H. Is Bitcoin a hedge or safe haven for currencies? An intraday analysis[J]. International Review of Financial Analysis, 2019, 63: 49-57.
    [27]
    LI X, WANG C A. The technology and economic determinants of cryptocurrency exchange rates: The case of Bitcoin[J]. Decision Support Systems, 2017, 95: 49-60.
    [28]
    KOENKER R, BASSETT Jr G. Regression quantiles[J]. Econometrica: Journal of the Econometric Society, 1978, 46: 33-50.
    [29]
    ANDREOU E, GHYSELS E, KOURTELLOS A. Regression models with mixed sampling frequencies[J]. Journal of Econometrics, 2010, 158(2): 246-261.
    [30]
    GHYSELS E, SINKO A, VALKANOV R. MIDAS regressions: Further results and new directions[J]. Econometric Reviews, 2007, 26(1): 53-90.
    [31]
    AKAIKE H. A new look at the statistical model identification[M]// Selected Papers of Hirotugu Akaike. New York: Springer, 1974: 215-222.
    [32]
    SCHWARZ G. Estimating the dimension of a model[J]. The Annals of Statistics, 1978, 6(2): 461-464.
    [33]
    YAO Q, TONG H. Asymmetric least squares regression estimation: A nonparametric approach[J]. Journal of Nonparametric Statistics, 1996, 6(2-3): 273-292.
    [34]
    BORRI N. Conditional tail-risk in cryptocurrency markets[J]. Journal of Empirical Finance, 2019, 50: 1-19.
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    [1]
    NEWEY W K, POWELL J L. Asymmetric least squares estimation and testing[J]. Econometrica: Journal of the Econometric Society, 1987, 55(4): 819-847.
    [2]
    KUAN C M, YEH J H, HSU Y C. Assessing value at risk with CARE, the conditional autoregressive expectile models[J]. Journal of Econometrics, 2009, 150(2): 261-270.
    [3]
    谢尚宇, 姚宏伟, 周勇. 基于 ARCH-Expectile 方法的 VaR 和 ES 尾部风险测量[J]. 中国管理科学, 2014, 22(9): 1-9.
    [4]
    XIE S, ZHOU Y, WAN A T K. A varying-coefficient expectile model for estimating value at risk[J]. Journal of Business & Economic Statistics, 2014, 32(4): 576-592.
    [5]
    KIM M, LEE S. Nonlinear expectile regression with application to value-at-risk and expected shortfall estimation[J]. Computational Statistics & Data Analysis, 2016, 94: 1-19.
    [6]
    谭常春, 操毅文, 叶五一. 基于 Expectile-based VaR 变点检测的金融传染分析[J]. 数理统计与管理, 2018, 37(2): 371-380.
    [7]
    DAOUIA A, GIRARD S, STUPFLER G. Extreme M-quantiles as risk measures: From L to Lp optimization[J]. Bernoulli, 2019, 25(1): 264-309.
    [8]
    许启发, 丁晓涵, 蒋翠侠. 基于 Expectile 回归的均值-ES组合投资决策[J]. 中国管理科学, 2018, 26(10): 20-29.
    [9]
    GHYSELS E, SANTA-CLARA P, VALKANOV R. The MIDAS touch: Mixed data sampling regression models[R]. CIRANO, 2004: 2004s-20.
    [10]
    GHYSELS E, SANTA-CLARA P, VALKANOV R. There is a risk-return trade-off after all[J]. Journal of Financial Economics, 2005, 76(3): 509-548.
    [11]
    MERTON R C. An intertemporal capital asset pricing model[J]. Econometrica, 1973, 41(5): 867-887.
    [12]
    GHYSELS E, SANTA-CLARA P, VALKANOV R. Predicting volatility: Getting the most out of return data sampled at different frequencies[J]. Journal of Econometrics, 2006, 131(1-2): 59-95.
    [13]
    GHYSELS E, PLAZZI A, VALKANOV R. Why invest in emerging markets? The role of conditional return asymmetry[J]. The Journal of Finance, 2016, 71(5): 2145-2192.
    [14]
    PETTENUZZO D, TIMMERMANN A, VALKANOV R. A MIDAS approach to modeling first and second moment dynamics[J]. Journal of Econometrics, 2016, 193(2): 315-334.
    [15]
    ANDREOU E. On the use of high frequency measures of volatility in MIDAS regressions[J]. Journal of Econometrics, 2016, 193(2): 367-389.
    [16]
    夏婷, 闻岳春. 经济不确定性是股市波动的因子吗?——基于 GARCH-MIDAS 模型的分析[J]. 中国管理科学, 2018, 26(12): 1-11.
    [17]
    尚玉皇, 郑挺国.短期利率波动测度与预测: 基于混频宏观-短期利率模型[J]. 金融研究, 2016(11): 47-62.
    [18]
    XU Q, WANG L, JIANG C, et al. A novel UMIDAS-SVQR model with mixed frequency investor sentiment for predicting stock market volatility[J]. Expert Systems with Applications, 2019, 132: 12-27.
    [19]
    AIGNER D J, AMEMIYA T, POIRIER D J. On the estimation of production frontiers: Maximum likelihood estimation of the parameters of a discontinuous density function[J]. International Economic Review, 1976,17(2): 377-396.
    [20]
    谢平, 石午光. 数字加密货币研究: 一个文献综述[J]. 金融研究, 2015(1): 1-15.
    [21]
    BUCHHOLZ M, DELANEY J, WARREN J, et al. Bits and bets, information, price volatility, and demand for Bitcoin[J]. Economics, 2012, 312: 2-48.
    [22]
    VAN WIJK D. What can be expected from the BitCoin[R]. Rotterdam, Netherlands: Erasmus Universiteit Rotterdam, 2013.
    [23]
    KRISTOUFEK L. What are the main drivers of the Bitcoin price? Evidence from wavelet coherence analysis[J]. PLoS ONE, 2015, 10(4): e0123923.
    [24]
    WALTHER T, KLEIN T. Exogenous drivers of cryptocurrency volatility: A mixed data sampling approach to forecasting[R]. St. Gallen, Switzerland: University of St. Gallen, 2018.
    [25]
    FRY J, CHEAH E T. Negative bubbles and shocks in cryptocurrency markets[J]. International Review of Financial Analysis, 2016, 47: 343-352.
    [26]
    URQUHART A, ZHANG H. Is Bitcoin a hedge or safe haven for currencies? An intraday analysis[J]. International Review of Financial Analysis, 2019, 63: 49-57.
    [27]
    LI X, WANG C A. The technology and economic determinants of cryptocurrency exchange rates: The case of Bitcoin[J]. Decision Support Systems, 2017, 95: 49-60.
    [28]
    KOENKER R, BASSETT Jr G. Regression quantiles[J]. Econometrica: Journal of the Econometric Society, 1978, 46: 33-50.
    [29]
    ANDREOU E, GHYSELS E, KOURTELLOS A. Regression models with mixed sampling frequencies[J]. Journal of Econometrics, 2010, 158(2): 246-261.
    [30]
    GHYSELS E, SINKO A, VALKANOV R. MIDAS regressions: Further results and new directions[J]. Econometric Reviews, 2007, 26(1): 53-90.
    [31]
    AKAIKE H. A new look at the statistical model identification[M]// Selected Papers of Hirotugu Akaike. New York: Springer, 1974: 215-222.
    [32]
    SCHWARZ G. Estimating the dimension of a model[J]. The Annals of Statistics, 1978, 6(2): 461-464.
    [33]
    YAO Q, TONG H. Asymmetric least squares regression estimation: A nonparametric approach[J]. Journal of Nonparametric Statistics, 1996, 6(2-3): 273-292.
    [34]
    BORRI N. Conditional tail-risk in cryptocurrency markets[J]. Journal of Empirical Finance, 2019, 50: 1-19.
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