Impact analysis of VaR methodologies on regulatory capital

Lampros Kalyvas, Athanasios Sfetsos

Abstract

ABSTRACT

In an attempt to predict volatility and value-at-risk (VaR) of financial returns, academic research has focused on the construction of complex models for the capture of heteroskedasticity. From aspect of view of credit institutions, performance evaluation of models is conducted by examining the ratio of times "the reality exceeds the prediction of VaR" over an observation period. If the mean ratio for several non-overlapping observation periods is below the required confidence level, the model is considered adequate. On the other hand, the multiplication factor produced under the guidelines of the Basel Committee is based on the absolute number of exceptions observed over a year. Volatility for some financial products is capable of deterministically predicting the VaR for the next day. However, the VaR for some products which demonstrate a non-linear relationship between the underlying risk factors and the product values exhibit a chaotic behavior that is hard to be predicted, when volatility increases above a certain threshold. The present work focuses on assessing these characteristics for different products, utilizing the concept of sample entropy (SamEn). It is proved that conditional models, even if heteroskedasticity is apparent, may be of no use beyond a certain level of volatility, depending on the nature of the product. Alternatively, "straight-forward" unconditional models are proposed for comparable cases.