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Closed-form approximation of American options


  • Bjerksund, Petter
  • Stensland, Gunnar


This paper presents a closed-form approximation of the value of the finite-lived American option where the underlying asset provides a constant pay-out rate. It is derived by imposing a restriction on the set of feasible exercise strategies, and thus represents a lower bound to the option value. The exercise strategy is to exercise the option the first time the price of the underlying asset hits a flat boundary. Our numerical results show that this lower bound is very close to the true option value.

Suggested Citation

  • Bjerksund, Petter & Stensland, Gunnar, 1993. "Closed-form approximation of American options," Scandinavian Journal of Management, Elsevier, vol. 9(Supplemen), pages 87-99.
  • Handle: RePEc:eee:scaman:v:9:y:1993:i:supplement1:p:s87-s99

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    References listed on IDEAS

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    Cited by:

    1. Haas, Markus & Mittnik, Stefan & Mizrach, Bruce, 2006. "Assessing central bank credibility during the ERM crises: Comparing option and spot market-based forecasts," Journal of Financial Stability, Elsevier, vol. 2(1), pages 28-54, April.
    2. Basili, Marcello & Fontini, Fulvio, 2012. "Biofuel from Jatropha curcas: Environmental sustainability and option value," Ecological Economics, Elsevier, vol. 78(C), pages 1-8.
    3. Bruce Mizrach, 2007. "Recovering Probabilistic Information From Options Prices and the Underlying," Departmental Working Papers 200702, Rutgers University, Department of Economics.
    4. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    5. Azusa Takeyama & Nick Constantinou & Dmitri Vinogradov, 2012. "A Framework for Extracting the Probability of Default from Stock Option Prices," IMES Discussion Paper Series 12-E-14, Institute for Monetary and Economic Studies, Bank of Japan.
    6. Minqiang Li, 2010. "Analytical approximations for the critical stock prices of American options: a performance comparison," Review of Derivatives Research, Springer, vol. 13(1), pages 75-99, April.
    7. repec:spr:annopr:v:260:y:2018:i:1:d:10.1007_s10479-016-2267-4 is not listed on IDEAS
    8. Bruce Mizrach, 2002. "When Did The Smart Money in Enron Lose Its' Smirk?," Departmental Working Papers 200224, Rutgers University, Department of Economics.
    9. Vinicius Albani & Uri M. Ascher & Jorge P. Zubelli, 2016. "Local Volatility Models in Commodity Markets and Online Calibration," Papers 1602.04372,
    10. Jennergren, L. Peter & Naslund, Bertil, 1996. "A class of options with stochastic lives and an extension of the Black-Scholes formula," European Journal of Operational Research, Elsevier, vol. 91(2), pages 229-234, June.
    11. Nils Crasselt & Christian Lohmann, 2016. "Considering real options in short-term decision making," Journal of Management Control: Zeitschrift für Planung und Unternehmenssteuerung, Springer, vol. 27(4), pages 351-369, November.
    12. Chorn, L.G. & Shokhor, S., 2006. "Real options for risk management in petroleum development investments," Energy Economics, Elsevier, vol. 28(4), pages 489-505, July.
    13. Jongwoo Lee & Dean Paxson, 2003. "Confined exponential approximations for the valuation of American options," The European Journal of Finance, Taylor & Francis Journals, vol. 9(5), pages 449-474.
    14. Pier Giuseppe Giribone & Simone Ligato, 2016. "Flexible-forward pricing through Leisen–Reimer trees: Implementation and performance comparison with traditional Markov chains," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 1-21, June.
    15. Lindset, Snorre & Lund, Arne-Christian, 2007. "A Monte Carlo approach for the American put under stochastic interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1081-1105, April.
    16. Bruce Mizrach, 2006. "The Enron Bankruptcy: When did the options market in Enron lose it’s smirk?," Review of Quantitative Finance and Accounting, Springer, vol. 27(4), pages 365-382, December.
    17. Francisco Venegas Martínez, 2001. "Opciones, cobertura y procesos de difusión con saltos: Una aplicación a los títulos de Gcarso," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 16(2), pages 203-226.
    18. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.


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