Sergio Bianchi

A novel methodology is introduced to dynamically analyze the complex scaling behavior of financial data across various investment horizons. This approach comprises two steps: (a) the application of a distribution-based method for the estimation of time-varying self-similarity matrices. These matrices consist of entries that represent the scaling parameters relating pairs of distributions of price changes constructed for different temporal scales (or investment horizons); (b) the utilization of information theory, specifically the Normalized Compression Distance, to quantify the relative complexity and ascertain the similarities between pairs of self-similarity matrices. Through this methodology, distinct patterns can be identified and they may delineate the levels and the composition of market liquidity. An application to the U.S. stock index S&P500 shows the effectiveness of the proposed methodology.

A new computational approach based on the pointwise regularity exponent of the price time series is proposed to estimate Value at Risk. The forecasts obtained are compared with those of two largely used methodologies: the variance-covariance method and the exponentially weighted moving average method. Our findings show that in two very turbulent periods of financial markets the forecasts obtained using our algorithm decidedly outperform the two benchmarks, providing more accurate estimates in terms of both unconditional coverage and independence and magnitude of losses.