Value at risk estimation with entropy-based wavelet analysis in exchange markets

• We incorporate the heterogeneous market structure information into the modeling process.
• We use the multivariate wavelet analysis to analyze multiscale heterogeneous behaviors of bivariate FX price.
• Mixture of underlying data components is modeled with different specifications and parameters.
• We use minimum error entropy criteria to choose wavelet families and decomposition level.
• The VaR estimation reliability improves at the statistically significant level.

In recent years, exchange markets are increasingly integrated together. Fluctuations and risks across different exchange markets exhibit co-moving and complex dynamics. In this paper we propose the entropy-based multivariate wavelet based approaches to analyze the multiscale characteristic in the multidimensional domain and improve further the Value at Risk estimation reliability. Wavelet analysis has been introduced to construct the entropy-based Multiscale Portfolio Value at Risk estimation algorithm to account for the multiscale dynamic correlation. The entropy measure has been proposed as the more effective measure with the error minimization principle to select the best basis when determining the wavelet families and the decomposition level to use. The empirical studies conducted in this paper have provided positive evidence as to the superior performance of the proposed approach, using the closely related Chinese Renminbi and European Euro exchange market.