On a generalised model for time-dependent variance with long-term memory

The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process captures the so-called "volatility clustering" and the asymptotic power-law probability density distribution of the random variable, it is not capable to reproduce further statistical properties of many of these time series such as: the strong persistence of the instantaneous variance characterised by large values of the Hurst exponent (H > 0.8), and asymptotic power-law decay of the absolute values self-correlation function. By means of considering an effective return obtained from a correlation of past returns that has a q-exponential form we are able to fix the limitations of the original model. Moreover, this improvement can be obtained through the correct choice of a sole additional parameter, $q_{m}$. The assessment of its validity and usefulness is made by mimicking daily fluctuations of SP500 financial index.Comment: 6 pages, 4 figure

Time connectedness of fear

This paper examines the interconnection between four implied volatility indices representative of the investors' consensus view of expected stock market volatility at different maturities during the period January 3, 2011-May 4, 2018. To this end, we first perform a static analysis to measure the total volatility connectedness in the entire period using a framework proposed by Diebold and Yilmaz (2014). Second, we apply a dynamic analysis to evaluate both the net directional connectedness for each market using the TVP-VAR connectedness approach developed by Antonakakis and Gabauer (2017). Our results suggest that a 72.27%, of the total variance of the forecast errors is explained by shocks across the examined investor time horizons, indicating that the remainder 27.73% of the variation is due to idiosyncratic shocks. Furthermore, we find that volatility connectedness varies over time, with a surge during periods of increasing economic and financial instability. Finally, we also document a superior performance of the TVP-VAR approach to connectedness respect to the original one proposed by Diebold and Yilmaz (2014