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valuation of options on joint minima and maxima

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Author Info

  • Tristan Guillaume

Abstract

It is shown how to obtain explicit formulae for a variety of popular path-dependent contracts with complex payoffs involving joint distributions of several extrema. More specifically, formulae are given for standard step-up and stepdown barrier options, as well as partial and outside step-up and step-down barrier options, between three and five dimensions. The proposed method can be extended to other exotic path-dependent payoffs as well as to higher dimensions. Numerical results show that the quasi-random integration of these formulae, involving multivariate distributions of correlated Gaussian random variables, provides option values more quickly and more accurately than Monte Carlo simulation.

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File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210122384
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 8 (2001)
Issue (Month): 4 ()
Pages: 209-233

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Handle: RePEc:taf:apmtfi:v:8:y:2001:i:4:p:209-233

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Related research

Keywords: Dimensionality; Joint Extrema; Step Barrier Options; Quasi-RANDOM Integration;

References

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  1. P. Carr, 1995. "Two extensions to barrier option valuation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 173-209.
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Cited by:
  1. Grant Armstrong, 2001. "Valuation formulae for window barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 197-208.
  2. Tristan Guillaume, 2011. "Some sequential boundary crossing results for geometric Brownian motion and their applications in financial engineering," Post-Print hal-00924277, HAL.

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