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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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    1. Yong-Ki Ma, 2015. "Modeling the Dependency Structure of Integrated Intensity Processes," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-10, August.
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    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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