A Generalized Normal Mean Variance Mixture For Return Processes In Finance

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Executive Summary

Time-changed Brownian motions are extensively applied as mathematical models for asset returns in Finance. Time change is interpreted as a switch to trade-related business time, different from calendar time. Time-changed Brownian motions can be generated by infinite divisible normal mixtures. The standard multivariate normal mean variance 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.

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