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valuation of options on joint minima and maxima

Author

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  • 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.

Suggested Citation

  • Tristan Guillaume, 2001. "valuation of options on joint minima and maxima," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 209-233.
    • Handle: RePEc:taf:apmtfi:v:8:y:2001:i:4:p:209-233
    DOI: 10.1080/13504860210122384
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    References listed on IDEAS

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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.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Tristan Guillaume, 2011. "Some sequential boundary crossing results for geometric Brownian motion and their applications in financial engineering," Post-Print hal-00924277, HAL.
    2. Grant Armstrong, 2001. "Valuation formulae for window barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 197-208.
    3. Lee, Hangsuck & Lee, Gaeun & Song, Seongjoo, 2023. "Min–max multi-step barrier options and their variants," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).

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