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

Author

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

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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  • Rudra P. Jena & Kyoung-Kuk Kim & Hao Xing, 2010. "Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions," Papers 1010.2865, arXiv.org, revised May 2012.
    • Handle: RePEc:arx:papers:1010.2865
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    File URL: http://arxiv.org/pdf/1010.2865
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    Cited by:

    1. Xiaowei Zhang & Peter W. Glynn, 2018. "Affine Jump-Diffusions: Stochastic Stability and Limit Theorems," Papers 1811.00122, arXiv.org.
    2. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2013. "Stationarity and ergodicity for an affine two factor model," Papers 1302.2534, arXiv.org, revised Sep 2013.
    3. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2012. "On parameter estimation for critical affine processes," Papers 1210.1866, arXiv.org, revised Mar 2013.

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