The Mixed Tempered Stable distribution (MixedTS) recently introduced has as special cases parametric distributions used in asset return modelling such as the Variance Gamma (VG) and Tempered Stable. In this paper, we start from this flexible distribution and compare the historical estimates for the two homogeneous risk measures with the quantities obtained using direct numerical integration and the saddle-point approximation. The homogeneity property enables us to go further and look for the most important sources of risk. Although risk decomposition in a parametric context is not straightforward, modified versions of VaR and ES based on asymptotic expansions simplify the problem.

Mercuri, L., Rroji, E. (2014). Risk measurement using the mixed tempered stable distribution. In C. Perna, M. Sibillo (a cura di), Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp. 137-140). Springer International Publishing [10.1007/978-3-319-05014-0_32].

### Risk measurement using the mixed tempered stable distribution

#### Abstract

The Mixed Tempered Stable distribution (MixedTS) recently introduced has as special cases parametric distributions used in asset return modelling such as the Variance Gamma (VG) and Tempered Stable. In this paper, we start from this flexible distribution and compare the historical estimates for the two homogeneous risk measures with the quantities obtained using direct numerical integration and the saddle-point approximation. The homogeneity property enables us to go further and look for the most important sources of risk. Although risk decomposition in a parametric context is not straightforward, modified versions of VaR and ES based on asymptotic expansions simplify the problem.
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Capitolo o saggio
Homogeneity; MixedTS; Risk decomposition;
English
Mathematical and Statistical Methods for Actuarial Sciences and Finance
Perna, C; Sibillo, M
2014
9783319050133
Springer International Publishing
137
140
Mercuri, L., Rroji, E. (2014). Risk measurement using the mixed tempered stable distribution. In C. Perna, M. Sibillo (a cura di), Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp. 137-140). Springer International Publishing [10.1007/978-3-319-05014-0_32].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/180605`