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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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TL;DR: In this paper, the transition probabilities of a class of subordinator motions with Laplace exponent vary regularly at infinity with index one with respect to the rank of the subspace of the subordinator.
Abstract: In this article we study transition probabilities of a class of subordinate Brownian motions. Under mild assumptions on the Laplace exponent of the corresponding subordinator, sharp two sided estimates of the transition probability are established. This approach, in particular, covers subordinators with Laplace exponents that vary regularly at infinity with index one, e.g. φ(λ) = λ log(1 + λ) − 1 or φ(λ) = λ log(1 + λβ/2) , β ∈ (0, 2) that correspond to subordinate Brownian motions with scaling order that is not necessarily stricty between 0 and 2. These estimates are applied to estimate Green function (potential) of subordinate Brownian motion. We also prove the equivalence of the lower scaling condition of the Laplace exponent and the near diagonal upper estimate of the transition estimate.

44 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider the time-changed Ornstein-Uhlenbeck process, in which time is replaced by an inverse subordinator of general infinite divisible distribution.
Abstract: The Ornstein–Uhlenbeck process is one of the most popular systems used for financial data description However, this process has also been examined in the context of many other phenomena In this paper we consider the so-called time-changed Ornstein–Uhlenbeck process, in which time is replaced by an inverse subordinator of general infinite divisible distribution Time-changed processes nowadays play an important role in various fields of mathematical physics, chemistry, and biology as well as in finance In this paper we examine the main characteristics of the time-changed Ornstein–Uhlenbeck process, such as the covariance function Moreover, we also prove the formula for a generalized fractional Fokker–Planck equation that describes the one-dimensional probability density function of the analyzed system For three cases of subordinators we show the special forms of obtained general formulas Furthermore, we mention how to simulate the trajectory of the Ornstein–Uhlenbeck process delayed by a general inverse subordinator

44 citations

Posted Content
TL;DR: In this paper, the authors investigate multivariate subordination with a common and an idiosyncratic component, and introduce generalizations of some well known univariate Levy processes for financial applications: the multivariate compound Poisson, NIG, Variance Gamma and CGMY.
Abstract: The traditional multivariate Levy process constructed by subordinating a Brownian motion through a univariate subordinator presents a number of drawbacks, including the lack of independence and a limited range of dependence. In order to face these, we investigate multivariate subordination, with a common and an idiosyncratic component. We introduce generalizations of some well known univariate Levy processes for financial applications: the multivariate compound Poisson, NIG, Variance Gamma and CGMY. In all these cases the extension is parsimonious, in that one additional parameter only is needed. We characterize first the subordinator, then the time changed processes via their Levy measure and characteristic exponent. We further study the subordinator association, as well as the subordinated processes linear and non linear dependence. We show that the processes generated with the proposed time change can include independence and that they span the whole range of linear dependence. We provide some examples of simulated trajectories,scatter plots and both linear and non linear dependence measures. The input data for these simulations are calibrated values for major stock indices.

44 citations

Journal ArticleDOI
TL;DR: In this article, the authors propose to extend the original model by relaxing the constraints on the subordinator parameters, leading to marginal characteristic functions which become a function of the whole parameter set.
Abstract: Luciano and Semeraro proposed a class of multivariate asset pricing models where the asset log-returns are modeled by a multivariate Brownian motion time-changed by a multivariate subordinator which consists of the weighted sum of a common and an idiosyncratic subordinator. In the original setting, Luciano and Semeraro imposed some constraints on the subordinator parameters such that the multivariate subordinator is of the same subordinator sub-class as its components, leading to asset log-returns of a particular Levy type. This restriction leads to marginal characteristic functions which are independent on the common subordinator setting. In this paper, we propose to extend the original model by relaxing the constraints on the subordinator parameters, leading to marginal characteristic functions which become a function of the whole parameter set. Under this generalized version, the volatility of the log-returns depends on both the common and idiosyncratic subordinator settings, and not only on the idiosyncratic one, which makes the generalized model more in line with the empirical evidence of the presence of both an idiosyncratic and a common component in the business clock. For the numerical study, we compare the calibration fit of both univariate option surfaces and market implied correlations for a period extending from the 2nd of June 2008 until the 30th of October 2009 under the two model settings and assess the calibration risk arising from different calibration procedures by pricing traditional multivariate exotic options. In particular we show that the decoupling calibration procedure fails to accurately replicate the market dependence structure under the original model for highly correlated asset returns and we propose an alternative methodology which rests on a joint calibration of the univariate and the dependence structure and which leads to an accurate fit of the market reality under both the generalized and original models.

44 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that any subordinated process arising from a Brownian motion with drift and a selfdecomposable subordinator is self-decompositionable.

43 citations


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