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Some sequential boundary crossing results for geometric Brownian motion and their applications in financial engineering

Author

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  • Tristan Guillaume

    (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper provides new explicit results for some boundary crossing distributions in a multi-dimensional geometric Brownian motion framework when the boundary is a piecewise constant function of time. Among their various possible applications, they enable accurate and efficient analytical valuation of a large number of option contracts traded in the financial markets belonging to the classes of barrier and lookback options.

Suggested Citation

  • Tristan Guillaume, 2011. "Some sequential boundary crossing results for geometric Brownian motion and their applications in financial engineering," Post-Print hal-00924277, HAL.
    • Handle: RePEc:hal:journl:hal-00924277
    Note: View the original document on HAL open archive server: https://hal.science/hal-00924277
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    References listed on IDEAS

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    1. Hoi Ying Wong & Yue-Kuen Kwok, 2003. "Multi-asset barrier options and occupation time derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(3), pages 245-266.
    2. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    3. Hua He & William P. Keirstead & Joachim Rebholz, 1998. "Double Lookbacks," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 201-228, July.
    4. Choi, Changsun & Nam, Dougu, 2003. "Some boundary-crossing results for linear diffusion processes," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 281-291, April.
    5. Tristan Guillaume, 2003. "Window double barrier options," Post-Print hal-00924247, HAL.
    6. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298, October.
    7. Tristan Guillaume, 2001. "valuation of options on joint minima and maxima," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 209-233.
    8. Grant Armstrong, 2001. "Valuation formulae for window barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 197-208.
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