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2 results

  • A Note on ‘Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options’ by Tankov (2011)

  • Part of
  • Carole Bernard, Xiao Jiang, Steven Vanduffel
  • Journal:
    Journal of Applied Probability / Volume 49 / Issue 3 / September 2012
    Published online by Cambridge University Press:
    04 February 2016, pp. 866-875
    Print publication:
    September 2012
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  • Tankov (2011) improved the Fréchet bounds for a bivariate copula when its values on a compact subset of [0, 1]2 are given. He showed that the best possible bounds are quasi-copulas and gave a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that the bounds are copulas. We also show how this can be useful in portfolio selection. It turns out that finding a copula as a lower bound plays a key role in determining optimal investment strategies explicitly for investors with some type of state-dependent constraints.

  • Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options

  • Part of
  • Peter Tankov
  • Journal:
    Journal of Applied Probability / Volume 48 / Issue 2 / June 2011
    Published online by Cambridge University Press:
    14 July 2016, pp. 389-403
    Print publication:
    June 2011
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  • Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of [0, 1]2, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.