This paper introduces a new approach to modelling the conditional variance in a multivariate setting. It is essentially a combination of the popular GARCH model class with a spatial component, inspired by generalized space-time models. The resulting spatial GARCH model takes into account both...

Under Black-Scholes (BS) assumptions, empirical volatility and risk neutral volatility are given by a single parameter, which captures all aspects of risk. Inverting the model to extract implied volatility from an option's market price gives the market's forecast of future empirical volatility....

The capacity of input-output tables to reflect the structural peculiarities of an economy and to forecast, on this basis, its evolution, depends essentially on the characteristics of the matrix A matrix of I-O (or technical) coefficients. However, the temporal behaviour of these coefficients is...