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Options on Multiple Assets in a Mean-Reverting Model

Author

Listed:
  • Masahiko Egami
  • Tadao Oryu

Abstract

We solve two optimal stopping problems whose payoR functions are the maximum and the minimum of two state variables driven by the Ornstein-Uhlenbeck processes. We consider a class of problems where we obtain analytical solutions. Furthermore, by making use of the analytical results we study some properties of exercise regions including convexity, symmetry, and continuity.

Suggested Citation

  • Masahiko Egami & Tadao Oryu, 2010. "Options on Multiple Assets in a Mean-Reverting Model," Discussion papers e-10-005, Graduate School of Economics Project Center, Kyoto University.
    • Handle: RePEc:kue:dpaper:e-10-005
    as

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    File URL: http://www.econ.kyoto-u.ac.jp/projectcenter/Paper/e-10-005.pdf
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    References listed on IDEAS

    as
    1. Abel Cadenillas & Sudipto Sarkar & Fernando Zapatero, 2007. "Optimal Dividend Policy With Mean‐Reverting Cash Reservoir," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 81-109, January.
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    3. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    4. Mark Broadie & Jérôme Detemple, 1997. "The Valuation of American Options on Multiple Assets," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 241-286, July.
    5. Tristan Guillaume, 2008. "Making the best of best-of," Review of Derivatives Research, Springer, vol. 11(1), pages 1-39, March.
    6. Stephane Villeneuve, 1999. "Exercise regions of American options on several assets," Finance and Stochastics, Springer, vol. 3(3), pages 295-322.
    7. Erhan Bayraktar & Masahiko Egami, 2010. "On the One-Dimensional Optimal Switching Problem," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 140-159, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    American options on multiple assets; Optimal stopping; Mean-reverting model;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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