Typical approaches incorporating jumps in financial dynamics, such as the Variance Gamma and CGMY models, can be made to depart from the i.i.d. hypothesis by using a stochastic clock. In such a context, the introduction of a dispersion of the clock is equiva- lent to the introduction of a dispersion of the volatility itself. A distinct route that yields
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comparable features is that of adding a jump component to a stochastic volatility process, or of considering, in discrete time, leptokurtic innovations within a GARCH process. In this article, we take a third route and we provide a study on tempered multistable pro- cesses, which convey both jumps and autocorrelation from their very construction, and on some of their applications in finance. We obtain the multivariate characteristic function of the asymmetrical field-based tempered multistable process and we study the autocorrela- tions that stem from the use of this model. We concentrate on three types of applications in finance: we study the term structures of Value-at-Risk that can be obtained with this model, we perform a calibration on stock index data, and we also conduct a calibration on derivatives prices.