Forward-looking portfolio selection with multivariate non-Gaussian models |
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Authors: | Michele Leonardo Bianchi Gian Luca Tassinari |
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Institution: | 1. Regulation and Macroprudential Analysis Directorate, Bank of Italy, Via Milano 53, Rome 00184, Italy micheleleonardo.bianchi@bancaditalia.it;3. Department of Economics, Department of Statistical Sciences “Paolo Fortunati”, and Department of Management, University of Bologna, Piazza Scaravilli, 2, Bologna 40126, Italy |
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Abstract: | In this study, we suggest a portfolio selection framework based on time series of stock log-returns, option-implied information, and multivariate non-Gaussian processes. We empirically assess a multivariate extension of the normal tempered stable (NTS) model and of the generalized hyperbolic (GH) one by implementing an estimation method that simultaneously calibrates the multivariate time series of log-returns and, for each margin, the univariate observed one-month implied volatility smile. To extract option-implied information, the connection between the historical measure P and the risk-neutral measure Q, needed to price options, is provided by the multivariate Esscher transform. The method is applied to fit a 50-dimensional series of stock returns, to evaluate widely known portfolio risk measures and to perform a forward-looking portfolio selection analysis. The proposed models are able to produce asymmetries, heavy tails, both linear and non-linear dependence and, to calibrate them, there is no need for liquid multivariate derivative quotes. |
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Keywords: | Normal mean–variance mixtures Time-changed Brownian motion Multivariate non-Gaussian processes Portfolio risk measures Portfolio optimization |
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