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

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  • J. D. Deuschel
  • P. K. Friz
  • A. Jacquier
  • S. Violante
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    Abstract

    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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    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

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    1. Jim Gatheral & Antoine Jacquier, 2010. "Convergence of Heston to SVI," Papers 1002.3633, arXiv.org.
    2. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480.
    3. 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.
    4. S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12.
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