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Modeling Crypto Returns with Multivariate Affine Generalized Hyperbolic distribution

In this paper, we investigate the modeling of crypto returns using the Multivariate Affine Generalized Hyperbolic distribution (MAGH). The MAGH is a multivariate extension of the Generalized Hyperbolic distribution(GH). The GH distribution is itself a family of distributions that encompasses various well-known special cases (Normal Inverse Gaussian, Laplace, and student’s t-distribution). We review and compare the properties of the above distributions, mainly the generation of jump Levy processes.

The analysis results in a methodology to generate the scenarios based on correlated asset structure. Obtained model can capture the heavy tails (extreme events), which is common for crypto returns. The proposed approach includes the seasonality extraction from the time series returns and evaluates its significance. Furthermore, we investigate FTX bankruptcy and prove the stability of the model.