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1 results

  • Integrating Volatility Clustering Into Exponential Lévy Models

  • Part of
  • Christian Bender, Tina Marquardt
  • Journal:
    Journal of Applied Probability / Volume 46 / Issue 3 / September 2009
    Published online by Cambridge University Press:
    14 July 2016, pp. 609-628
    Print publication:
    September 2009
    • Article
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  • We introduce a class of stock models that interpolates between exponential Lévy models based on Brownian subordination and certain stochastic volatility models with Lévy-driven volatility, such as the Barndorff-Nielsen–Shephard model. The driving process in our model is a Brownian motion subordinated to a business time which is obtained by convolution of a Lévy subordinator with a deterministic kernel. We motivate several choices of the kernel that lead to volatility clusters while maintaining the sudden extreme movements of the stock. Moreover, we discuss some statistical and path properties of the models, prove absence of arbitrage and incompleteness, and explain how to price vanilla options by simulation and fast Fourier transform methods.