A central component of the Basel III (B3) document is the "Sound practices for backtesting", i.e., a summary of strict regulatory guidances on how to validate and backtest Internal Method Models (IMM) for credit exposure. In the present work, we define a complete statistical framework to...

The correlations among assets returns is one of the key components in the construction of a diversified portfolio. It has been observed though that in time of great distress, when a drop in financial markets occurs, correlations tend to increase. As a consequence, the diversification effect is...

A new approach is presented to describe the change in the statistics of the log return distribution of financial data as a function of the timescale. To this purpose a measure is introduced, which quantifies the distance of a considered distribution to a reference distribution. The existence of...

A stochastic analysis of financial data is presented. In particular we investigate how the statistics of log returns change with different time delays τ. The scale-dependent behaviour of financial data can be divided into two regions. The first time range, the small-timescale region (in the...