Topic
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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15 Aug 2019
TL;DR: In this article, the authors extend the classical constant elasticity of variance (CEV) model to a subdiffusive CEV model, where the underlying CEV process is time changed by an inverse α-stable subordinator.
Abstract: In this paper, we extend the classical constant elasticity of variance (CEV) model to a subdiffusive CEV model, where the underlying CEV process is time changed by an inverse α-stable subordinator....
5 citations
17 Jul 2021
TL;DR: In this paper, the authors define a subordinator by means of the lower-incomplete gamma function, which can be considered as an approximation of the stable subordinator, easier to be handled in view of its finite activity.
Abstract: We start by defining a subordinator by means of the lower-incomplete gamma function. This can be considered as an approximation of the stable subordinator, easier to be handled in view of its finite activity. A tempered version is also considered in order to overcome the drawback of infinite moments. Then, we study Levy processes that are time-changed by these subordinators with particular attention to the Brownian case. An approximation of the fractional derivative (as well as of the fractional power of operators) arises from the analysis of governing equations. Finally, we show that time-changing the fractional Brownian motion produces a model of anomalous diffusion, which exhibits a sub-diffusive behavior.
5 citations
TL;DR: In this paper, two constructions of fractal activity time in the fractal Activity Time geometric Brownian motion (FATGBM) model for a risky asset are discussed, which produce tractable dependence structure that includes long-range dependence.
Abstract: Two constructions of fractal activity time in the fractal activity time geometric Brownian motion (FATGBM) model for a risky asset are discussed. Both constructions produce tractable dependence structure that includes long-range dependence. One construction uses Ornstein-Uhlenbeck type processes and leads to stationary log returns with exact normal tempered stable distribution and pricing formula that is based on the asymptotic self-similarity of the activity time. The second construction uses convoluted subordinator with Holmgren-Liouville kernel and leads to exact pricing formula that is based on exact tempered stable distribution of the activity time. Option prices computed using our model and pricing formulae are remarkably close to the real market values.
5 citations
01 Jan 1995
TL;DR: The results of Fristedt and Pruitt [6,7] on the lower functions of a subordinator are improved in the case when the Laplace exponent is slowly varying as mentioned in this paper, yielding laws of the iterated logarithm for the local times of a class of Markov processes.
Abstract: Results of Fristedt and Pruitt [6,7] on the lower functions of a subordinator are improved in the case when the Laplace exponent is slowly varying. This yields laws of the iterated logarithm for the local times of a class of Markov processes. In particular, this extends recent results of Marcus and Rosen [9] on certain Levy processes close to a Cauchy process.
5 citations
15 Sep 2008
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
5 citations