Evolving Possibilistic Fuzzy Modeling and Application in Value-at-Risk Estimation

Abstract

This chapter suggests an evolving possibilistic fuzzy modeling approach for value-at-risk modeling and estimation. The modeling approach is based on an extension of the possibilistic fuzzy c-means clustering and functional fuzzy rule-based systems. It employs memberships and typicalities to update clusters centers and creates new clusters using a statistical control distance-based criteria. Evolving possibilistic fuzzy modeling (ePFM) also uses an utility measure to evaluate the quality of the current cluster structure. The fuzzy rule-based model emerges from the cluster structure. Market risk exposure plays a key role for financial institutions in risk assessment and management. A way to measure risk exposure is to evaluate the losses likely to incur when the prices of the portfolio assets decline. Value-at-risk (VaR) estimate is amongst the most prominent measure of financial downside market risk. Computational experiments are conducted to evaluate ePFM for value-at-risk estimation using data of the main equity market indexes of United States (S&P 500) and Brazil (Ibovespa) from January 2000 to December 2012. Econometric models benchmarks such as GARCH and EWMA, and state of the art evolving approaches are compared against ePFM. The results suggest that ePFM is a potential candidate for VaR modeling and estimation because it achieves higher performance than econometric and alternative evolving approaches.