Stochastic Volatility Effects on Correlated Log-Normal Random Variables

Stochastic Volatility Effects on Correlated Log-Normal Random Variables

The transition density function plays an important role in understanding and explaining the dynamics of the stochastic process. In this paper, we incorporate an ergodic process displaying fast moving fluctuation into constant volatility models to express volatility clustering over time. We obtain an...

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Main Author: Yong-Ki Ma
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2017/7150203
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spelling doaj-575b99d8756f464aa3a3597524f532ca2021-07-02T05:46:48ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/71502037150203Stochastic Volatility Effects on Correlated Log-Normal Random VariablesYong-Ki Ma0Department of Applied Mathematics, Kongju National University, Chungcheongnam-do 32588, Republic of KoreaThe transition density function plays an important role in understanding and explaining the dynamics of the stochastic process. In this paper, we incorporate an ergodic process displaying fast moving fluctuation into constant volatility models to express volatility clustering over time. We obtain an analytic approximation of the transition density function under our stochastic process model. Using perturbation theory based on Lie–Trotter operator splitting method, we compute the leading-order term and the first-order correction term and then present the left and right skew scenarios through numerical study.http://dx.doi.org/10.1155/2017/7150203
collection DOAJ
language English
format Article
sources DOAJ
author Yong-Ki Ma
spellingShingle Yong-Ki Ma
Stochastic Volatility Effects on Correlated Log-Normal Random Variables
Advances in Mathematical Physics
author_facet Yong-Ki Ma
author_sort Yong-Ki Ma
title Stochastic Volatility Effects on Correlated Log-Normal Random Variables
title_short Stochastic Volatility Effects on Correlated Log-Normal Random Variables
title_full Stochastic Volatility Effects on Correlated Log-Normal Random Variables
title_fullStr Stochastic Volatility Effects on Correlated Log-Normal Random Variables
title_full_unstemmed Stochastic Volatility Effects on Correlated Log-Normal Random Variables
title_sort stochastic volatility effects on correlated log-normal random variables
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2017-01-01
description The transition density function plays an important role in understanding and explaining the dynamics of the stochastic process. In this paper, we incorporate an ergodic process displaying fast moving fluctuation into constant volatility models to express volatility clustering over time. We obtain an analytic approximation of the transition density function under our stochastic process model. Using perturbation theory based on Lie–Trotter operator splitting method, we compute the leading-order term and the first-order correction term and then present the left and right skew scenarios through numerical study.
url http://dx.doi.org/10.1155/2017/7150203
work_keys_str_mv AT yongkima stochasticvolatilityeffectsoncorrelatedlognormalrandomvariables
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