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Time-Changed Fast Mean-Reverting Stochastic Volatility Models

Author

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  • MATTHEW LORIG

    (Department of Operations Research & Financial Engineering, Princeton University, Princeton, NJ 08544, USA)

Abstract

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility (TC-FMR-SV) models. Using spectral theory and singular perturbation techniques, we derive an approximation for the price of any European option in the TC-FMR-SV setting. Three examples of random time-changes are provided and are shown to induce distinct implied volatility surfaces. The key features of the TC-FMR-SV framework are that (i) it is able to incorporate jumps into the price process of the underlying asset (ii) it allows for the leverage effect and (iii) it can accommodate multiple factors of volatility, which operate on different time-scales.

Suggested Citation

  • Matthew Lorig, 2011. "Time-Changed Fast Mean-Reverting Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(08), pages 1355-1383.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:08:n:s0219024911006875
    DOI: 10.1142/S0219024911006875
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    Cited by:

    1. Borovkova, Svetlana & Schmeck, Maren Diane, 2017. "Electricity price modeling with stochastic time change," Energy Economics, Elsevier, vol. 63(C), pages 51-65.
    2. Likuan Qin & Vadim Linetsky, 2014. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery and Long-Term Pricing," Papers 1411.3075, arXiv.org, revised Sep 2015.
    3. Likuan Qin & Vadim Linetsky, 2016. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery, and Long-Term Pricing," Operations Research, INFORMS, vol. 64(1), pages 99-117, February.

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