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Stochastic Volatility Effects on Correlated Log‐Normal Random Variables

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  • Yong-Ki Ma

Abstract

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.

Suggested Citation

  • Yong-Ki Ma, 2017. "Stochastic Volatility Effects on Correlated Log‐Normal Random Variables," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    • Handle: RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:7150203
    DOI: 10.1155/2017/7150203
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    References listed on IDEAS

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