Quasi maximum likelihood estimation of Value at Risk (VaR) and Expected Shortfall (ES) is discussed. The reference likelihood is that of a location-scale asymmetric Laplace distribution, related to a family of loss functions that lead to strictly consistent scoring functions for joint estimation...

This paper shows that different states of the financial system command a different effect in worsening financial conditions on economic vulnerability. As soon as financial conditions start deteriorating, the economic outlook becomes more pessimistic and uncertain. No increase in macroeconomic...

This paper addresses the problem of estimating multiple quantiles from a time series. A flexible class of dynamic multiple quantile (DMQ) models is specified, ensuring that estimated quantiles do not cross and that extreme quantiles are estimated by exploiting information coming from all the...

This paper studies the leverage effect and its propagation over time. We show that common volatility models like the GJRGARCH, the Exponential GARCH, and the asymmetric SV can be inappropriate to correctly represent the leverage effect and its propagation for financial time series. We propose to...

We present a new modelling framework for the bi-variate hidden Markov model. The proposed specification is composed by five latent Markovian chains which drive the evolution of the parameters of a bi-variate Gaussian distribution. The maximum likelihood estimator is computed via an expectation...

This paper studies the behaviour of Bitcoin returns at different sample frequencies. We consider high frequency returns starting from tick-by-tick price changes traded at the Bitstamp and Coinbase exchanges. We find evidence of a smooth intra-daily seasonality pattern, and an abnormal trade- and...