Multifractal Value at Risk model

In this paper new Value at Risk (VaR) model is proposed and investigated. We consider the multifractal property of financial time series and develop a multifractal Value at Risk (MFVaR). MFVaR introduced in this paper is analytically tractable and not based on simulation. Empirical study showed that MFVaR can provide the more stable and accurate forecasting performance in volatile financial markets where large loss can be incurred. This implies that our multifractal VaR works well for the risk measurement of extreme credit events.

[1]  Xincheng Xie,et al.  Quantum phase transitions and coherent tunneling in a bilayer of ultracold atoms with dipole interactions , 2012 .

[2]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[3]  D. Sornette,et al.  Multifractal returns and hierarchical portfolio theory , 2000, cond-mat/0008069.

[4]  T. Aste,et al.  Multi-scale correlations in different futures markets , 2007, 0707.3321.

[5]  Laurent E. Calvet,et al.  A Multifractal Model of Asset Returns , 1997 .

[6]  Laurent E. Calvet,et al.  Forecasting Multifractal Volatility , 1999 .

[7]  H. Stanley,et al.  A multifractal analysis of Asian foreign exchange markets , 2008 .

[8]  Minimum Risk Portfolios Using MMAR , 2009 .

[9]  Laurent E. Calvet,et al.  Multifractality in Asset Returns: Theory and Evidence , 2002, Review of Economics and Statistics.

[10]  D. Grech,et al.  Can one make any crash prediction in finance using the local Hurst exponent idea , 2003, cond-mat/0311627.

[11]  Emmanuel Bacry,et al.  Continuous cascade models for asset returns , 2008 .

[12]  B. Mandelbrot Fractals and Scaling In Finance: Discontinuity, Concentration, Risk , 2010 .

[13]  A. Barabasi,et al.  Fractal concepts in surface growth , 1995 .

[14]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[15]  Niklas Wagner,et al.  Multifractality and value-at-risk forecasting of exchange rates , 2014 .

[16]  T. Aste,et al.  Understanding the source of multifractality in financial markets , 2012, 1201.1535.

[17]  Hojin Lee,et al.  Multifractal regime detecting method for financial time series , 2015 .

[18]  Petre Caraiani,et al.  Evidence of Multifractality from Emerging European Stock Markets , 2012, PloS one.

[19]  Sunil Kumar,et al.  Multifractal properties of the Indian financial market , 2009 .

[20]  T. D. Matteo,et al.  Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series , 2011, 1109.0465.

[21]  Yu Wei,et al.  Forecasting volatility of SSEC in Chinese stock market using multifractal analysis , 2008 .

[22]  A. Sensoy Time-varying long range dependence in market returns of FEAS members , 2013 .

[23]  E. Bacry,et al.  Multifractal random walk. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Alejandra Figliola,et al.  A multifractal approach for stock market inefficiency , 2008 .

[25]  O. Rosso,et al.  Multifractal structure in Latin-American market indices , 2009 .

[26]  D. Grech,et al.  The local Hurst exponent of the financial time series in the vicinity of crashes on the Polish stock exchange market , 2008 .

[27]  Tomaso Aste,et al.  Non-stationary multifractality in stock returns , 2013 .

[28]  Thomas Lux,et al.  The Markov-Switching Multifractal Model of Asset Returns , 2008 .

[29]  Tomaso Aste,et al.  Scaling behaviors in differently developed markets , 2003 .

[30]  A. Sensoy,et al.  Generalized Hurst exponent approach to efficiency in MENA markets , 2013 .

[31]  Armin Bunde,et al.  Improved risk estimation in multifractal records: Application to the value at risk in finance. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Laurent E. Calvet,et al.  Multifractal Volatility: Theory, Forecasting, and Pricing , 2008 .

[33]  Boris Podobnik,et al.  Detrended cross-correlation analysis for non-stationary time series with periodic trends , 2011 .