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Real Options and American Derivatives: the Double Continuation Region

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  • Anna Battauz
  • Marzia De Donno
  • Alessandro Sbuelz
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    Abstract

    We thoroughly study the non-standard optimal exercise policy associated with relevant capital investment options and with the prepayment option of widespread collateralized-borrowing contracts like the gold loan. Option exercise is optimally postponed not only when moneyness is insufficient but also when it is excessive. We contribute an important extension of the classical optimal exercise properties for American options. Early exercise of an American call with a negative underlying payout rate can occur if the option is moderately in the money. We fully characterize the existence, the monotonicity, the continuity, the limits and the symptotic behavior at maturity of the double free boundary that separates the exercise region from the double continuation region. We fi?nd that the ?finite-maturity non-standard policy conspicuously differs from the infi?nite-maturity one. Keywords: American Options; Valuation; Optimal Exercise; Real Options; Gold Loan; Collateralized Borrowing; Asymptotic Approximation of The Free Boundary.

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    Bibliographic Info

    Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 499.

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    Date of creation: 2013
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    Handle: RePEc:igi:igierp:499

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    1. Damien Lamberton & Mohammed Mikou, 2008. "The critical price for the American put in an exponential Lévy model," Finance and Stochastics, Springer, Springer, vol. 12(4), pages 561-581, October.
    2. Carl Chiarella & Andrew Ziogas, 2002. "Evaluation of American Strangles," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 83, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. McDonald, Robert & Siegel, Daniel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 101(4), pages 707-27, November.
    4. Detemple, Jérôme & Emmerling, Thomas, 2009. "American chooser options," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(1), pages 128-153, January.
    5. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, Elsevier, vol. 98(1), pages 145-159, October.
    6. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, INFORMS, vol. 50(9), pages 1145-1177, September.
    7. J. D. Evans & R. Kuske & Joseph B. Keller, 2002. "American options on assets with dividends near expiry," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(3), pages 219-237.
    8. Anna Battauz & Marzia De Donno & Alessandro Sbuelz, 2012. "Real options with a double continuation region," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 12(3), pages 465-475, April.
    9. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-50.
    10. Schroder, Mark, 1999. "Changes of Numeraire for Pricing Futures, Forwards, and Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 12(5), pages 1143-63.
    11. Pindyck, Robert S, 1993. "A Note on Competitive Investment under Uncertainty," American Economic Review, American Economic Association, American Economic Association, vol. 83(1), pages 273-77, March.
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