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Subordinator

About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.


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Steven Kou1
29 Sep 2014
TL;DR: In this paper, an overview of properties related to Levy processes is given, and certain difficulties in applying Levy processes, such as the volatility clustering effect and those in distinguishing the tail behavior of asset returns, are also discussed.
Abstract: After mentioning empirical motivation of Levy processes in asset pricing, an overview of properties related to Levy processes is given. Certain difficulties in applying Levy processes, such as the volatility clustering effect and those in distinguishing the tail behavior of asset returns, are also discussed. Keywords: leptokurtic distribution; jump diffusion; subordinator; infinite activity Levy processes; volatility clustering effect; tail distribution

4 citations

Journal ArticleDOI
TL;DR: In this paper, saddlepoint approximations for general subordinator processes were derived for the Poisson processes, the Gamma process, the α-stable subordinators, and the poisson random integrals.
Abstract: We develop the saddlepoint approximations in obtaining the transition functions for general subordinator processes. We derive explicit expressions of the first- and second-order approximations. Specifically, we consider some particular classes of subordinators including the Poisson processes, the Gamma processes, the α-stable subordinators, and the Poisson random integrals. We test this technique on the Poisson and Gamma processes, which have closed-form transition functions. Outcomes show that the approximate expressions are consistent with the true transition functions. We then use this method to predict transition density functions for the α-stable subordinator processes. Finally, we calculate approximated transition densities for some Poisson random integrations. Numerical analysis shows the perfect ability of the saddlepoint approximations to predict the transition densities of the α-stable processes and the Poisson random integrations.

4 citations

Journal ArticleDOI
TL;DR: In this paper, the Doob transformation rule is applied to a time-changed Gauss-Markov process and a fractional pseudo-Fokker-Planck equation is given.
Abstract: We consider some time-changed diffusion processes obtained by applying the Doob transformation rule to a time-changed Brownian motion. The time-change is obtained via the inverse of an α-stable subordinator. These processes are specified in terms of time-changed Gauss-Markov processes and fractional time-changed diffusions. A fractional pseudo-Fokker-Planck equation for such processes is given. We investigate their first passage time densities providing a generalized integral equation they satisfy and some transformation rules. First passage time densities for time-changed Brownian motion and Ornstein-Uhlenbeck processes are provided in several forms. Connections with closed form results and numerical evaluations through the level zero are given.

4 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied higher-order moment measures of heavy-tailed renewal models, including a renewal point process with heavy-tail inter-renewal distribution and its continuous analog, the occupation measure of a heavytailed Levy subordinator, and revealed that the asymptotic structure of such moment measures are given by explicit power-law density functions.
Abstract: We study higher-order moment measures of heavy-tailed renewal models, including a renewal point process with heavy-tailed inter-renewal distribution and its continuous analog, the occupation measure of a heavy-tailed Levy subordinator. Our results reveal that the asymptotic structure of such moment measures are given by explicit power-law density functions. The same power-law densities appear naturally as cumulant measures of certain Poisson and Gaussian stochastic integrals. This correspondence provides new and extended results regarding the asymptotic fluctuations of heavy-tailed sources under aggregation, and clarifies existing links between renewal models and fractional random processes.

4 citations

Journal ArticleDOI
TL;DR: In this paper, the authors compared the shape of pairwise default correlations of the Hull & White, the Gaussian copula and the Mai & Scherer model with compound Poisson process as Levy subordinator.
Abstract: In this paper, some analytical results related to the Hull & White dynamic model of credit portfolio of N obligors in the case of constant jump size are provided. For instance, this specific assumption combined with the moment generating function of the Poisson process lead to analytical calibration for the model with respect to the underlying CDSs. Further, extremely simple analytical expressions are obtained for first-to-default swaps; the more general case of quantities related to 'n'th-to-default swaps also have a closed form and remain tractable for small n. Similarly, pairwise correlation between default indicators also proves to be simple. Although the purpose of this note is not to compare models, we compare the shape of pairwise default correlations of the Hull & White, the Gaussian copula and the Mai & Scherer model with compound Poisson process as Levy subordinator. It is shown that only the models including jumps can lead to non-vanishing default correlation for short-term maturities. Further, these models can generate higher default correlation levels compared to the Gaussian one. When calibrated on default probability of first default time, Jump-based models also lead to much higher default probability for the last obligor to default. Finally, we tackle the problem of simultaneous jumps, which prevent the above class of models to be usable when recoveries are name-specific. To that end, we propose a tractable compromise to deal with baskets being non-homogeneous recovery-wise under the Hull & White model by splitting isolated and non-isolated default events.

4 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202330
202242
202160
202056
201969
201845