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Time-Changed Fast Mean-Reverting Stochastic Volatility Models

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  • MATTHEW LORIG

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

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    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.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 14 (2011)
    Issue (Month): 08 ()
    Pages: 1355-1383

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    Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:08:p:1355-1383

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    Related research

    Keywords: Stochastic volatility; stochastic time-change; implied volatility; levy subordinator; jump-diffusion; multiscale;

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