Probabilistic fuzzy systems in value-at-risk estimation

Value-at-risk (VaR) is a popular measure for quantifying the market risk that a financial institution faces into a single number. Owing to the complexity of financial markets, the risks associated with a portfolio varies over time. Consequently, advanced methods of VaR estimation use parametric conditional models of portfolio volatility (e.g. generalized autoregressive heteroscedasticity (GARCH) models) to adapt risk estimation to changing market conditions. However, more flexible semi-parametric methods that adapt to the highly flexible underlying data distribution are better suited for accurate VaR estimation. In this paper, we consider VaR estimation by using probabilistic fuzzy systems (PFSs). A PFS is a semi-parametric method that combines a linguistic description of the system behaviour with statistical properties of the data. Therefore, they provide the potential to adapt estimations of probability density to the linguistic framework of the modeller. We study two approaches to designing probabilistic fuzzy VaR models and compare their performances with the performance of a GARCH model. It is found that statistical back testing always accepts PFS models after tuning, whereas GARCH models may be rejected. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  Umberto Cherubini,et al.  Fuzzy Value-at-risk: Accounting for Market Liquidity , 2001 .

[2]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[3]  R. Cont.  Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models. , 2005 .

[4]  Paul H. Kupiec,et al.  Techniques for Verifying the Accuracy of Risk Measurement Models , 1995 .

[5]  Zdeněk Zmeškal.  Value at risk methodology of international index portfolio under soft conditions (fuzzy-stochastic approach) , 2005 .

[6]  Zdenek Zmeskal.  Value at risk methodology under soft conditions approach (fuzzy-stochastic approach) , 2005, Eur. J. Oper. Res..

[7]  Uzay Kaymak,et al.  Maximum likelihood parameter estimation in probabilistic fuzzy classifiers , 2005, The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05..

[8]  Zvi Wiener.  Introduction to Var (Value-At-Risk) , 1999 .

[9]  James W. Taylor.  A Quantile Regression Neural Network Approach to Estimating the Conditional Density of Multiperiod Returns , 2000 .

[10]  Uzay Kaymak,et al.  Financial markets analysis by using a probabilistic fuzzy modelling approach , 2004, Int. J. Approx. Reason..

[11]  Nicolas Chapados,et al.  Cost functions and model combination for VaR-based asset allocation using neural networks , 2001, IEEE Trans. Neural Networks.

[12]  Monica Billio,et al.  Value-at-Risk: a multivariate switching regime approach , 2000 .

[13]  D. Duffie,et al.  An Overview of Value at Risk , 1997 .

[14]  Uzay Kaymak,et al.  A fuzzy additive reasoning scheme for probabilistic Mamdani fuzzy systems , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[15]  Gary L. Gastineau.  Some Derivatives Accountsing Issues , 1995 .