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Constant Elasticity Of Variance In Random Time: A New Stochastic Volatility Model With Path Dependence And Leverage Effect

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  • DMITRY OSTROVSKY

    (RBS Greenwich Capital, 600 Steamboat Road, Greenwich, CT 06830, USA)

Abstract

An arbitrage-free CEV economy driven by Brownian motion in independent, continuous random time is introduced. European options are priced by the no-arbitrage principle as conditional averages of their classical CEV values over the CEV-modified random time to maturity. A novel representation of the classical CEV price is used to investigate the asymptotics of the average implied volatility. It is shown that the average implied volatility of the at-the-money call option is lower and of deep out-of-the-money call options, under appropriate sufficient conditions, greater than the implied CEV volatilities. Unlike in the classical CEV model, the shape of the out-of-the-money tail can be both downward and upward sloping depending on the tails of random time. The model is implemented in limit lognormal time. Its multiscaling law is shown to imply a term structure of implied volatility that is qualitatively more sensitive to changes in the time to maturity than is the classical CEV model.

Suggested Citation

  • Dmitry Ostrovsky, 2007. "Constant Elasticity Of Variance In Random Time: A New Stochastic Volatility Model With Path Dependence And Leverage Effect," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(06), pages 915-937.
    • Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:06:n:s0219024907004494
    DOI: 10.1142/S0219024907004494
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    References listed on IDEAS

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    1. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
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