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Marginal density expansions for diffusions and stochastic volatility, part II: Applications [to the Stein--Stein model]

  • J. D. Deuschel
  • P. K. Friz
  • A. Jacquier
  • S. Violante
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    In the compagnion paper [Marginal density expansions for diffusions and stochastic volatility, part I] we discussed density expansions for multidimensional diffusions $(X^1,...,X^d)$, at fixed time $T$ and projected to their first $l$ coordinates, in the small noise regime. Global conditions were found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptotics. In the present paper we discuss financial applications; these include tail and implied volatility asymptotics in some correlated stochastic volatility models. In particular, we solve a problem left open by A. Gulisashvili and E.M. Stein (2009).

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    File URL: http://arxiv.org/pdf/1305.6765
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    Paper provided by arXiv.org in its series Papers with number 1305.6765.

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    Date of creation: May 2013
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    Handle: RePEc:arx:papers:1305.6765
    Contact details of provider: Web page: http://arxiv.org/

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    1. Jim Gatheral & Antoine Jacquier, 2010. "Convergence of Heston to SVI," Papers 1002.3633, arXiv.org.
    2. S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12.
    3. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480.
    4. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
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