Hawkes Processes have been finding more applications in diverse areas of science, engineering and quantitative finance. In multi-frequency finance, various phenomena have been observed, such as shocks, crashes, volatility clustering, turbulent flows and contagion. Hawkes processes have been...

This paper introduces a new methodology for an alternative calculation of market volatility index based on a multinomial tree approximation of a stochastic volatility model. The estimation is performed by constructing synthetic options with consistent properties. Several variants of this index...

In this work we present a methodology to detect rare events which are defined as large price movements relative to the volume traded. We analyze the behavior of equity after the detection of these rare events. We provide methods to calibrate trading rules based on the detection of these events...