Mixed Tempered Stable Distribution

Rroji, Edit; Mercuri, Lorenzo

doi:10.2139/ssrn.2339273

Cited by 4 publications

(12 citation statements)

References 24 publications

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“…As shown in Rroji and Mercuri (), if V ∼Γ( a , b ), we get some well‐known distributions used for modeling financial returns as special cases. For instance, if α =2, the Variance Gamma introduced in Madan and Seneta () is obtained.…”

Section: Univariate Mixed Tempered Stablementioning

confidence: 94%

“…Suppose F is an infinitely divisible distribution on

{double-struckR}_{+}

with cumulant function Φ V . Then, there is a convolution semigroup of probability measures ( F t ) t ⩾0 on

{double-struckR}_{+}

and a Lévy process ( V t ) t ⩾0 such that V t ∼ F t for t ⩾0 and

{normal Φ}_{V_{t}} (u) = t {normal Φ}_{V} (u)

.In Rroji and Mercuri (), it is shown that the

M i x e d T S ((), μ t, β, α, λ_{+}, λ_{-}) - F_{t}

distribution is infinitely divisible. According to the general theory, see, for example, proposition 3.1, p. 69 in Cont and Tankov (), there exists a Lévy process ( Y t ) t ⩾0 such that

Y_{1} \sim M i x e d T S ((), μ, β, α, λ_{+}, λ_{-}) - F_{1}

.…”

Section: Univariate Mixed Tempered Stablementioning

confidence: 99%

“…The Mixed Tempered Stable (MixedTS from now on) distribution has been introduced in Rroji and Mercuri () and used for portfolio selection in Hitaj et al () and for option pricing in Mercuri and Rroji (). It is a generalisation of the Normal Variance Mean Mixtures (see Barndorff‐Nielsen et al ., ) given that the structure is similar but its definition generates a dependence of higher moments on the parameters of the standardised Classical Tempered Stable (CTS)(see Küchler & Tappe, ; Kim et al ., ) that replaces the Normal distribution.Recently, different multivariate distributions have been introduced in literature for modeling the joint dynamics of financial time series.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Properties of the MixedTS Distribution and Its Multivariate Extension

Hitaj

Hubalek

Mercuri

et al. 2018

Int Statistical Rev

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A review of the univariate MixedTS is given and some new results on the asymptotic tail behaviour are derived. The multivariate version of the Mixed Tempered Stable, which is a generalisation of the Normal Variance Mean Mixtures, is discussed. Characteristics of this distribution, its capacity in fitting tails and in capturing dependence structure between components are investigated. We discuss a random number generating procedure and introduce an estimation methodology based on the minimisation of a distance between empirical and theoretical characteristic functions. Asymptotic tail behaviour of the univariate Mixed Tempered Stable is exploited in the estimation procedure in order to obtain a better fitting on tails. Advantages of the multivariate Mixed Tempered Stable distribution are discussed and illustrated via numerical analysis.

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Section: Univariate Mixed Tempered Stablementioning

confidence: 94%

“…Suppose F is an infinitely divisible distribution on

{double-struckR}_{+}

with cumulant function Φ V . Then, there is a convolution semigroup of probability measures ( F t ) t ⩾0 on

{double-struckR}_{+}

and a Lévy process ( V t ) t ⩾0 such that V t ∼ F t for t ⩾0 and

{normal Φ}_{V_{t}} (u) = t {normal Φ}_{V} (u)

.In Rroji and Mercuri (), it is shown that the

M i x e d T S ((), μ t, β, α, λ_{+}, λ_{-}) - F_{t}

distribution is infinitely divisible. According to the general theory, see, for example, proposition 3.1, p. 69 in Cont and Tankov (), there exists a Lévy process ( Y t ) t ⩾0 such that

Y_{1} \sim M i x e d T S ((), μ, β, α, λ_{+}, λ_{-}) - F_{1}

.…”

Section: Univariate Mixed Tempered Stablementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Properties of the MixedTS Distribution and Its Multivariate Extension

Hitaj

Hubalek

Mercuri

et al. 2018

Int Statistical Rev

Self Cite

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show abstract

“…By modifying the Lévy measure of a stable law, we can introduce the tempered stable family from both univariate and multivariate perspectives (Boyarchenko and Levendorskiȋ (2000) and Boyarchenko and Levendorskiȋ (2002)). Formal and elegant definitions of tempered stable distributions and processes were proposed in the seminal study by Rosiński (2007) who employed a completely monotone function to transform the Lévy measure of a stable distribution (various parametric classes were discussed by Terdik and Woyczynski (2006), Bianchi et al (2010), Bianchi (2015), Rroji and Mercuri (2015), Grabchak (2016)). Two classes of distributions that are broader than the tempered stable class have been proposed, where Rosinski and Singlair (2010) introduced the generalised tempered stable class and Grabchak (2012) proposed the p-tempered stable class.…”

Section: Literature Reviewmentioning

confidence: 99%

Modeling Tail Risk with Tempered Stable Distributions: An Overview

Fallahgoul

Loeper

2018

SSRN Journal

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“…The main object of this paper is to present an option pricing model under the assumption that log returns are generated from a Lévy Mixed Tempered Stable (MixedTS hereafter) process. This process is built using the infinitely divisible property of the MixedTS distribution recently introduced by Rroji and Mercuri (2015) as a generalization of the Normal Variance Mean Mixture (NVMM hereafter) family of distributions. The relevance of Lévy processes has been widely investigated in financial modeling especially for asset prices (Carr and Wu, 2004a;Eberlein and Madan, 2009;Carr and Madan, 1999, see for instance) mainly due to the fact that these processes are able to handle with the stylized facts.…”

Section: Introductionmentioning

confidence: 99%