The statistical estimate of the branching ratio η of the Hawkes model, when fitted to windows of mid-price changes, has been reported to approach criticality (η = 1) as the fitting window becomes large. In this study -- using price changes from the EUR/USD currency pair traded on the...

For a weighted sum of asset returns that are independent and identically distributed (IID) up to variance, we derive expressions linking the distribution of variance across assets with higher-order portfolio moments, assuming these quantities are finite. In particular, we show concise...

We introduce a new framework for understanding portfolio diversification that provides a coherent basis for comparing methodologies and offers a new approach to portfolio construction. The primary argument is that measures of diversification based only on a covariance matrix are ambiguous...

The first ever explicit formulation of the concept of the option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True...

In recent years, fractionally-differenced processes have received a great deal of attention due to their flexibility in financial applications with long-memory. This paper revisits the class of generalized fractionally-differenced processes generated by Gegenbauer polynomials and the ARMA...

The first ever explicit formulation of the concept of an option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True Value-at-Risk...