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The Valuation of American Options on Multiple Assets

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  • Mark Broadie
  • Jér�me Detemple
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    Abstract

    In this paper we provide valuation formulas for several types of American options on two or more assets. Our contribution is twofold. First, we characterize the optimal exercise regions and provide valuation formulas for a number of American option contracts on multiple underlying assets with convex payoff functions. Examples include options on the maximum of two assets, dual strike options, spread options, exchange options, options on the product and powers of the product, and options on the arithmetic average of two assets. Second, we derive results for American option contracts with nonconvex payoffs, such as American capped exchange options. For this option we explicitly identify the optimal exercise boundary and provide a decomposition of the price in terms of a capped exchange option with automatic exercise at the cap and an early exercise premium involving the benefits of exercising prior to reaching the cap. Besides generalizing the current literature on American option valuation our analysis has implications for the theory of investment under uncertainty. A specialization of one of our models also provides a new representation formula for an American capped option on a single underlying asset. Copyright Blackwell Publishers Inc. 1997.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 7 (1997)
    Issue (Month): 3 ()
    Pages: 241-286

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    Handle: RePEc:bla:mathfi:v:7:y:1997:i:3:p:241-286

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    Cited by:
    1. Michi Nishihara & Takashi Sshibata, 2011. "Investment timing with fixed and proportional costs of external financing," Discussion Papers in Economics and Business 11-29, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP).
    2. Jeroen V.K. Rombouts & Lars Stentoft, 2010. "Multivariate Option Pricing with Time Varying Volatility and Correlations," Cahiers de recherche 1020, CIRPEE.
    3. Jérôme B. Detemple, 1999. "American Options: Symmetry Properties," CIRANO Working Papers 99s-45, CIRANO.
    4. Marti G. Subrahmanyam & Bin Gao & Jing-zhi Huang, 1998. "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-067, New York University, Leonard N. Stern School of Business-.
    5. Gerald Cheang & Carl Chiarella, 2011. "Exchange Options Under Jump-Diffusion Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(3), pages 245-276.
    6. Yoram Landskroner & Alon Raviv, 2004. "The Valuation of Inflation-Indexed and FX Convertible Bonds," Finance 0401005, EconWPA.
    7. Nishihara, Michi & Shibata, Takashi, 2013. "The effects of external financing costs on investment timing and sizing decisions," Journal of Banking & Finance, Elsevier, vol. 37(4), pages 1160-1175.
    8. Min Dai & Zuo Quan Xu, 2009. "Optimal Redeeming Strategy of Stock Loans," Papers 0906.0702, arXiv.org.
    9. Michi NISHIHARA & Takashi SHIBATA, 2012. "The effects of external financing costs on investment timing and sizing decisions," Discussion Papers in Economics and Business 12-07, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP).
    10. 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.
    11. Michi Nishihara, 2010. "A model for determining whether a firm should exercise multiple real options individually or simultaneously," Discussion Papers in Economics and Business 10-12, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP).
    12. Alfredo Ibáñez, 2003. "Robust Pricing of the American Put Option: A Note on Richardson Extrapolation and the Early Exercise Premium," Management Science, INFORMS, vol. 49(9), pages 1210-1228, September.
    13. Doan, Viet_Dung & Gaikwad, Abhijeet & Bossy, Mireille & Baude, Françoise & Stokes-Rees, Ian, 2010. "Parallel pricing algorithms for multi-dimensional Bermudan/American options using Monte Carlo methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 568-577.
    14. Detemple, Jérôme & Emmerling, Thomas, 2009. "American chooser options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 128-153, January.
    15. Jin, Xing & Li, Xun & Tan, Hwee Huat & Wu, Zhenyu, 2013. "A computationally efficient state-space partitioning approach to pricing high-dimensional American options via dimension reduction," European Journal of Operational Research, Elsevier, vol. 231(2), pages 362-370.
    16. Dean Paxson, 2007. "Sequential American Exchange Property Options," The Journal of Real Estate Finance and Economics, Springer, vol. 34(1), pages 135-157, January.
    17. Garcia, Diego, 2003. "Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1855-1879, August.

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