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Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions

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  • Rudra P. Jena
  • Kyoung-Kuk Kim
  • Hao Xing
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    Abstract

    This paper considers multi-dimensional affine processes with continuous sample paths. By analyzing the Riccati system, which is associated with affine processes via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time. In these two cases, we also compute the long-term growth rate and the explosion rate for exponential moments. These results provide a handle to study implied volatility asymptotics in models where returns of stock prices are described by affine processes whose exponential moments do not have an explicit formula.

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    File URL: http://arxiv.org/pdf/1010.2865
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1010.2865.

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    Date of creation: Oct 2010
    Date of revision: May 2012
    Handle: RePEc:arx:papers:1010.2865

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    Web page: http://arxiv.org/

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