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Real Options and American Derivatives: the Double Continuation Region

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  • Anna Battauz
  • Marzia De Donno
  • Alessandro Sbuelz

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.

Suggested Citation

  • Anna Battauz & Marzia De Donno & Alessandro Sbuelz, 2013. "Real Options and American Derivatives: the Double Continuation Region," Working Papers 499, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:499
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    Cited by:

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    2. Gapeev, Pavel V., 2020. "Optimal stopping problems for running minima with positive discounting rates," LSE Research Online Documents on Economics 105849, London School of Economics and Political Science, LSE Library.
    3. Marzia De Donno & Zbigniew Palmowski & Joanna Tumilewicz, 2020. "Double continuation regions for American and Swing options with negative discount rate in Lévy models," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 196-227, January.
    4. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    5. Trigeorgis, Lenos & Tsekrekos, Andrianos E., 2018. "Real Options in Operations Research: A Review," European Journal of Operational Research, Elsevier, vol. 270(1), pages 1-24.
    6. Detemple, Jérôme & Laminou Abdou, Souleymane & Moraux, Franck, 2020. "American step options," European Journal of Operational Research, Elsevier, vol. 282(1), pages 363-385.
    7. Ludovic Mathys, 2019. "Valuing Tradeability in Exponential L\'evy Models," Papers 1912.00469, arXiv.org, revised Feb 2020.
    8. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    9. Zbigniew Palmowski & José Luis Pérez & Kazutoshi Yamazaki, 2021. "Double continuation regions for American options under Poisson exercise opportunities," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 722-771, April.
    10. Zbigniew Palmowski & Jos'e Luis P'erez & Kazutoshi Yamazaki, 2020. "Double continuation regions for American options under Poisson exercise opportunities," Papers 2004.03330, arXiv.org.
    11. C. E. Phelan & D. Marazzina & G. Germano, 2020. "Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities," Quantitative Finance, Taylor & Francis Journals, vol. 20(6), pages 899-918, June.
    12. Delaney, L., 2016. "Equilibrium Investment in High Frequency Trading Technology: A Real Options Approach," Working Papers 15/14, Department of Economics, City University London.
    13. Kirkby, J. Lars & Nguyen, Duy & Cui, Zhenyu, 2017. "A unified approach to Bermudan and barrier options under stochastic volatility models with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 75-100.
    14. Anna Battauz & Marzia De Donno & Janusz Gajda & Alessandro Sbuelz, 2022. "Optimal exercise of American put options near maturity: A new economic perspective," Review of Derivatives Research, Springer, vol. 25(1), pages 23-46, April.
    15. Carolyn E. Phelan & Daniele Marazzina & Guido Germano, 2021. "Pricing methods for $\alpha$-quantile and perpetual early exercise options based on Spitzer identities," Papers 2106.06030, arXiv.org.
    16. Delaney, Laura, 2018. "Investment in high-frequency trading technology: A real options approach," European Journal of Operational Research, Elsevier, vol. 270(1), pages 375-385.
    17. Jonas Al-Hadad & Zbigniew Palmowski, 2020. "Perpetual American options with asset-dependent discounting," Papers 2007.09419, arXiv.org, revised Jan 2021.
    18. Shuaiqiang Liu & 'Alvaro Leitao & Anastasia Borovykh & Cornelis W. Oosterlee, 2020. "On Calibration Neural Networks for extracting implied information from American options," Papers 2001.11786, arXiv.org.
    19. Battauz, Anna & De Donno, Marzia & Sbuelz, Alessandro, 2022. "On the exercise of American quanto options," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).

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