A Modified Tempered Stable Distribution with Volatility Clustering

Kim, Y.S.; Rachev, Svetlozar T.; Chung, Dong Myung; Bianchi, Michele Leonardo

doi:10.5848/csp.1155.00014

Cited by 25 publications

(26 citation statements)

References 18 publications

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“…The NTS distribution was originally obtained using a time-changed Brownian motion with a temperedstable subordinator by Barndorff-Nielsen and Levendorski (2001), then later reconstructed in Kim et al (2009) by exponential tilting of a symmetric modified tempered stable distribution. BarndorffNielsen and Shephard (2001) noted its heavy tails and identified it as a special case of the normal inverse Gaussian (NIG) distribution.…”

Section: Normal Truncated Stable Modelsmentioning

confidence: 99%

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

Goode

Kim

Fabozzi³

2015

Applied Economics

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We compare the backtesting performance of ARMA-GARCH models with the most common types of infinitely divisible innovations, fit with both full maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE). The innovation types considered are the Gaussian, Student's t, α-stable, classical tempered stable (CTS), normal tempered stable (NTS) and generalized hyperbolic (GH) distributions. In calm periods of decreasing volatility, MLE and QMLE produce near identical performance in forecasting value-at-risk (VaR) and conditional value-at-risk (CVaR). In more volatile periods, QMLE can actually produce superior performance for CTS, NTS and α-stable innovations. While the t-ARMA-GARCH model has the fewest number of VaR violations, rejections by the Kupeic and Berkowitz tests suggest excessively large forecasted losses. The α-stable, CTS and NTS innovations compare favourably, with the latter two also allowing for option pricing under a single market model.

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Section: Normal Truncated Stable Modelsmentioning

confidence: 99%

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

Goode

Kim

Fabozzi³

2015

Applied Economics

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“…Tempered α-stable processes posses very important feature, namely, they have finite moments of all orders but, at the same time, they resemble stable laws in many aspects (see [24] for details). We can name many fields of applications of such processes, finance [26,27], biology [28], physics in the description of anomalous diffusion (especially when one observes the transition from the initial subdiffusive character of motion in short times to standard diffusion in long times) [29,30,31]. Since tempered α-stable processes are extension of α-stable ones, the tempered derivatives are a natural extension of fractional ones.…”

Section: Tempered Fractional Derivativesmentioning

confidence: 99%

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Gajda¹

2012

Acta Phys. Pol. B

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We develop a new class of continuous-time models based on the solutions of tempered fractional Langevin equations for Ornstein-Uhlenbeck process driven by Lévy noise. We present methods of simulation of sample paths of such processes. We show how to use such models in modeling short term interest rate. We develop tempered Vasiček interest rate model by finding explicit solutions of tempered fractional Langevin equations.

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“…Motivated by Pipiras and Taqqu [1], this work serves to generalize this asymptotic behavior related to a general class of infinitely divisible processes which encompasses standard Poissonized telecom processes [2], layered stable processes [3], generalized tempered stable processes [4], modified tempered stable distributions [5], and Lamperti stable processes [6]. Processes of this type have exhibited a broad range of applications in numerous fields, such as ''statistical physics, queuing theory, and mathematical finance'' [3].…”

Section: Introductionmentioning

confidence: 99%

A generalization result regarding the small and large scale behavior of infinitely divisible processes

Sinclair

2013

Journal of Mathematical Analysis and Applications

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a b s t r a c tGeneral conditions for normalized, time-scaled stochastic integrals of independently scattered Levy random measures to converge to a limit are described. The idea is to provide general conditions to bypass the use of characteristic functions, which can sometimes have tedious calculations, to simplify and shorten the proofs of convergence of infinitely divisible processes, which have previously been done on a case by case basis. It is of particular interest to study both small and large scale asymptotics, since there are many applications, such as modeling internet traffic. The purpose of this paper is to generalize previous results to the greater class of all stochastically continuous (or, more generally, separable in probability) infinitely divisible processes with no Gaussian part and to expand the results to the multi-dimensional case.

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A Modified Tempered Stable Distribution with Volatility Clustering

Cited by 25 publications

References 18 publications

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

Untitled

A generalization result regarding the small and large scale behavior of infinitely divisible processes

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