多重分形模型及其在金融风险管理中的应用述评
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摘要
金融市场的实证研究显示,金融数据除了尖峰厚尾、波动率集聚等特点,还具有多重分形特征。目前风险建模中普遍采用的GARCH族模型不能反映这一特征,容易导致估计偏差。多重分形模型能够更好地拟合金融时间序列,但在中国金融问题研究中的应用较少。首先回顾了应用较广的资产收益多重分形模型、马尔科夫转换多重分形模型和多重分形随机游走模型,从理论和实证角度讨论模型在金融风险管理方面的研究优势以及建模过程中存在的不足之处,然后分别介绍其在金融风险研究领域的应用进展,最后指出三种模型可能的拓展方法和未来在金融风险管理中的应用方向。
Empirical research of financial markets showed that besides leptokurtosis,heavy tails,volatility clustering,et al.,financial data also exhibited multifractal feature.GARCH family models which werewidely applied in risk modeling could not reflect this feature and easily leaded to estimation bias.While it fitted financial time series better,multifractal models were seldom applied in China's financial researches.This paper first reviewed widely used multifractal model of asset returns,markov-switching multifractal model and multifractal random walk model,discussed their advantages in financial risk management from theoretical and empirical perspectives as well as limitations in modeling,then introduced their application progress in financial risk research.Finally,it pointed out models' possible improvement and future applied direction in financial risk management.
Empirical research of financial markets showed that besides leptokurtosis,heavy tails,volatility clustering,et al.,financial data also exhibited multifractal feature.GARCH family models which werewidely applied in risk modeling could not reflect this feature and easily leaded to estimation bias.While it fitted financial time series better,multifractal models were seldom applied in China's financial researches.This paper first reviewed widely used multifractal model of asset returns,markov-switching multifractal model and multifractal random walk model,discussed their advantages in financial risk management from theoretical and empirical perspectives as well as limitations in modeling,then introduced their application progress in financial risk research.Finally,it pointed out models' possible improvement and future applied direction in financial risk management.
引文
[1] Peters E E.Fractal Market Analysis:Applying Chaos Theory to Investment and Economics[M].New York:John Wiley & Sons,1994.
[2] Hadrien S,Roberto M,Elsa A.Multifractal Methodology[J].Physica A,2017(473).
[3] Mandelbrot B B,Fisher A,Calvet L.A Multifractal Model of Asset Returns[R].Cowles Foundation Discussion Paper,Yale University,1997.
[4] Calvet L,Fisher A.Forecasting Multifractal Volatility[J].Journal of Econometrics,2001,105(1).
[5] Bacry E,Delour J,Muzy J F.Multifractal Random Walk[J].Physical Review E,2001,64(2).
[6] Calvet L,Fisher A,Thompson S.Volatility Comovement:A Multifrequency Approach[J].Journal of Econometrics,2006(131).
[7] Lux T,Segnon M,Gupta R.Forecasting Crude Oil Price Volatility and Value-at-risk:Evidence from Historical and Recent Data[J].Energy Economics,2016 (56).
[8] Malo P.Modeling Electricity Spot and Futures Price Dependence:A Multifrequency Approach[J].Physica A,2009(22).
[9] Mawuli S,Mark T.Forecasting Market Risk of Portfolios:Copula-Markov Switching Multifractal Approach[J].The European Journal of Finance,2018,24(14).
[10] Herrera R,Rodriguez A,Pino G.Modeling and Forecasting Extreme Commodity Prices:A Markov-Switching Based Extreme Value Model[J].Energy Economics,2017 (63).
[11] Batten J A,Kinateder H,Wagner N.Multifractality and Value-at-risk Forecasting of Exchange Rates[J].Physica A,2014 (401).
[12] Lee H,Song J W,Chang W.Multifractal Value at Risk Model[J].Physica A,2016 (451).
[13] Bacry E,Kozhemyak A,Muzy J F.Continuous Cascade Models for Asset Returns[J].Journal of Economic Dynamics and Control,2008,32 (1).
[14] Bacry E,Kozhemyak A,Muzy J F.Log-normal Continuous Cascade Model of Asset Returns:Aggregation Properties and Estimation[J].Quantitative Finance,2013,13 (5).
[15] Günay S.Performance of the Multifractal Model of Asset Returns (MMAR):Evidence from Emerging Stock Markets[J].International Journal of Financial Studies,2016,4(2).
[16] Liu R P,Lux T.Non-homogeneous Volatility Correlations in the Bivariate Multifractal Model[J].The European Journal of Finance,2015,21 (12).
[17] Ben N A,Lux T,Ajmi A N,et al.Forecasting the Volatility of the Dow Jones Islamic Stock Market Index:Long Memory vs.Regime Switching[J].International Review of Economics and Finance,2016(45).
[18] Muzy J F,Bacry E.Multifractal Stationary Random Measures and Multifractal Random Walks with Log Infinitely Divisible Scaling Laws[J].Physical Review E,2002(66).
[19] Bacry E,Muzy J F.Log-infinitely Divisible Multifractal Processes[J].Communications in Mathematical Physics,2003(236).
[20] Duchon J,Robert R,Vargas V.Forecasting Volatility with the Multifractal Random Walk Model[J].Mathematical Finance,2012,22(1).
[2] Hadrien S,Roberto M,Elsa A.Multifractal Methodology[J].Physica A,2017(473).
[3] Mandelbrot B B,Fisher A,Calvet L.A Multifractal Model of Asset Returns[R].Cowles Foundation Discussion Paper,Yale University,1997.
[4] Calvet L,Fisher A.Forecasting Multifractal Volatility[J].Journal of Econometrics,2001,105(1).
[5] Bacry E,Delour J,Muzy J F.Multifractal Random Walk[J].Physical Review E,2001,64(2).
[6] Calvet L,Fisher A,Thompson S.Volatility Comovement:A Multifrequency Approach[J].Journal of Econometrics,2006(131).
[7] Lux T,Segnon M,Gupta R.Forecasting Crude Oil Price Volatility and Value-at-risk:Evidence from Historical and Recent Data[J].Energy Economics,2016 (56).
[8] Malo P.Modeling Electricity Spot and Futures Price Dependence:A Multifrequency Approach[J].Physica A,2009(22).
[9] Mawuli S,Mark T.Forecasting Market Risk of Portfolios:Copula-Markov Switching Multifractal Approach[J].The European Journal of Finance,2018,24(14).
[10] Herrera R,Rodriguez A,Pino G.Modeling and Forecasting Extreme Commodity Prices:A Markov-Switching Based Extreme Value Model[J].Energy Economics,2017 (63).
[11] Batten J A,Kinateder H,Wagner N.Multifractality and Value-at-risk Forecasting of Exchange Rates[J].Physica A,2014 (401).
[12] Lee H,Song J W,Chang W.Multifractal Value at Risk Model[J].Physica A,2016 (451).
[13] Bacry E,Kozhemyak A,Muzy J F.Continuous Cascade Models for Asset Returns[J].Journal of Economic Dynamics and Control,2008,32 (1).
[14] Bacry E,Kozhemyak A,Muzy J F.Log-normal Continuous Cascade Model of Asset Returns:Aggregation Properties and Estimation[J].Quantitative Finance,2013,13 (5).
[15] Günay S.Performance of the Multifractal Model of Asset Returns (MMAR):Evidence from Emerging Stock Markets[J].International Journal of Financial Studies,2016,4(2).
[16] Liu R P,Lux T.Non-homogeneous Volatility Correlations in the Bivariate Multifractal Model[J].The European Journal of Finance,2015,21 (12).
[17] Ben N A,Lux T,Ajmi A N,et al.Forecasting the Volatility of the Dow Jones Islamic Stock Market Index:Long Memory vs.Regime Switching[J].International Review of Economics and Finance,2016(45).
[18] Muzy J F,Bacry E.Multifractal Stationary Random Measures and Multifractal Random Walks with Log Infinitely Divisible Scaling Laws[J].Physical Review E,2002(66).
[19] Bacry E,Muzy J F.Log-infinitely Divisible Multifractal Processes[J].Communications in Mathematical Physics,2003(236).
[20] Duchon J,Robert R,Vargas V.Forecasting Volatility with the Multifractal Random Walk Model[J].Mathematical Finance,2012,22(1).