A GENERALIZED NORMAL MEAN-VARIANCE MIXTURE FOR RETURN PROCESSES IN FINANCE

Time-changed Brownian motions are extensively applied as mathematical models for asset returns in Finance. Time change is interpreted as a switch from calendar time to trade-related business time. Time-changed Brownian motions can be generated by infinitely divisible normal mixtures. The standard multivariate mixtures assume a common mixing variable. This corresponds to a multidimensional return process with a unique change of time for all assets under exam. The economic counterpart is uniqueness of trade or business time, which is not in line with empirical evidence. In this paper we propose a new multivariate definition of normal mixtures with a flexible dependence structure, based on the economic intuition of both a common and an idiosyncratic component of business time. We analyze both the distribution and the related process. We use the above construction to introduce a multivariate generalized hyperbolic process with generalized hyperbolic margins. We conclude with a stock market example to show the ease of calibration of the model.