Multivariate time-varying volatility modeling using Probabilistic Fuzzy Systems

Methods to accurately analyze financial risk have drawn considerable attention in financial institutions. One difficulty in financial risk analysis is the fact that banks and other financial institutions invest in several assets which show time-varying volatilities and hence time-varying financial risk. In addition, these assets are typically correlated and the correlation between different assets may change over time. Such changes in the multivariate volatility structure of the assets lead to substantial changes in the financial risk of a portfolio held by the financial institution. Therefore analyzing changes in the volatility of assets in a multivariate setting is essential to document changing risk properties of financial institutions. In this paper we propose a Probabilistic Fuzzy System (PFS) to model the unobserved time-varying correlation between a large set of financial returns. We define a parsimonious PFS where the current pairwise correlations between assets depend on two antecedent variables, namely the minimum and maximum past correlation in the market. We exemplify the proposed PFS model in six pairwise correlations for four industry portfolios in the US and show that the proposed method captures time-varying pairwise correlations while keeping the antecedent space parsimonious. Furthermore, we show that a portfolio investor that invests in these US industries calculates a lower risk for his/her portfolio when time-varying correlation estimates are not taken into account.