Tempered Infinitely Divisible Distributions and Processes

Bianchi, Michele Leonardo; Rachev, Svetlozar T.; Kim, Young S.; Fabozzi, Frank J.

doi:10.1137/s0040585x97984632

Cited by 48 publications

(41 citation statements)

References 9 publications

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“…Tail tempering is achieved by modifying only the tails of stable distributions so that they remain thicker than the Gaussian tails but do not lead to an infinite volatility. The technique is described in Kim et al (2008), Kim et al (2010), and Bianchi et al (2010).…”

Section: Tempered Stable Distributionsmentioning

confidence: 99%

Fat-Tailed Models for Risk Estimation

Stoyanov¹,

Rachev²,

Racheva-Iotova³

et al. 2011

JPM

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In the post-crisis era, financial institutions seem to be more aware of the risks posed by extreme events. Even though there are attempts to adapt methodologies drawing from the vast academic literature on the topic, there is also skepticism that fat-tailed models are needed. In this paper, we address the common criticism and discuss three popular methods for extreme risk modeling based on full distribution modeling and and extreme value theory.

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Section: Tempered Stable Distributionsmentioning

confidence: 99%

Fat-Tailed Models for Risk Estimation

Stoyanov¹,

Rachev²,

Racheva-Iotova³

et al. 2011

JPM

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“…If a random variable X follows the RDTS distribution, then we denote X ∼ RDTS(α, Rosiński (2007), but included in the class of the tempered infinitely divisible distribution (Bianchi et al (2008)). …”

Section: Rapidly Decreasing Tempered Stable Distributionmentioning

confidence: 99%

“…The former belongs to the class proposed by Rosiński (2007) and has been already applied to option pricing with volatility clustering by Kim et al (2008a), the latter belongs to the class proposed by Bianchi et al (2008).…”

Section: Introductionmentioning

confidence: 99%

Tempered stable and tempered infinitely divisible GARCH models

Kim¹,

Rachev

Bianchi

et al. 2010

Journal of Banking & Finance

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Abstract. In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the non-zero skewness and excess kurtosis for the residual distribution. Furthermore, we review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, these GARCH models allow to find the risk-neutral price process, and hence they can be applied to option pricing. We propose algorithms to generate scenario based on GARCH models with CTS and RDTS innovation. To investigate the performance of these GARCH models, we report a parameters estimation for Dow Jones Industrial Average (DJIA) index and stocks included in this index, and furthermore to demonstrate their advantages, we calculate option prices based on these models. It should be noted that only historical data on the underlying asset and on the riskfree rate are taken into account to evaluate option prices.

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“…In particular, when p = 1 and α ∈ (0, 2), it coincides with Rosiński's [20] tempered stable distributions. When p = 2 and α ∈ [0, 2), it coincides with the class of 1016 M. GRABCHAK tempered infinitely divisible distributions defined in [6]. If we allow the distributions to have a Gaussian part then we would have the class J α,p defined in [16].…”

Section: Introductionmentioning

confidence: 97%

On a new Class of Tempered Stable Distributions: Moments and Regular Variation

Grabchak

2012

Journal of Applied Probability

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We extend the class of tempered stable distributions, which were first introduced in Rosiński (2007). Our new class allows for more structure and more variety of the tail behaviors. We discuss various subclasses and the relations between them. To characterize the possible tails, we give detailed results about finiteness of various moments. We also give necessary and sufficient conditions for the tails to be regularly varying. This last part allows us to characterize the domain of attraction to which a particular tempered stable distribution belongs.

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Tempered Infinitely Divisible Distributions and Processes

Cited by 48 publications

References 9 publications

Fat-Tailed Models for Risk Estimation

Fat-Tailed Models for Risk Estimation

Tempered stable and tempered infinitely divisible GARCH models

On a new Class of Tempered Stable Distributions: Moments and Regular Variation

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