TIME-CHANGED FAST MEAN-REVERTING STOCHASTIC VOLATILITY MODELS

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

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 08, 1355-1383

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.

Keywords: Stochastic volatility; stochastic time-change; implied volatility; levy subordinator; jump-diffusion; multiscale (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219024911006875

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