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Advances in Mathematical Physics
Volume 2017, Article ID 7150203, 7 pages
Research Article

Stochastic Volatility Effects on Correlated Log-Normal Random Variables

Department of Applied Mathematics, Kongju National University, Chungcheongnam-do 32588, Republic of Korea

Correspondence should be addressed to Yong-Ki Ma;

Received 12 July 2017; Revised 25 September 2017; Accepted 9 December 2017; Published 28 December 2017

Academic Editor: Antonio Scarfone

Copyright © 2017 Yong-Ki Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.