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Closed-form approximation of American options

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  • Bjerksund, Petter
  • Stensland, Gunnar

Abstract

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.

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File URL: http://www.sciencedirect.com/science/article/pii/095652219390009H
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Bibliographic Info

Article provided by Elsevier in its journal Scandinavian Journal of Management.

Volume (Year): 9 (1993)
Issue (Month): Supplement 1 ()
Pages: S87-S99

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Handle: RePEc:eee:scaman:v:9:y:1993:i:supplement1:p:s87-s99

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Related research

Keywords: American option approximation closed-form finite-lived lower bound;

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Cited by:
  1. Haas, Markus & Mittnik, Stefan & Mizrach, Bruce, 2005. "Assessing central bank credibility during the EMS crises: Comparing option and spot market-based forecasts," CFS Working Paper Series 2005/09, Center for Financial Studies (CFS).
  2. 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.
  3. 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.
  4. 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.
  5. Bruce Mizrach, 2007. "Recovering Probabilistic Information From Options Prices and the Underlying," Departmental Working Papers 200702, Rutgers University, Department of Economics.
  6. 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.
  7. 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.
  8. Bruce Mizrach, 2002. "When Did The Smart Money in Enron Lose Its' Smirk?," Departmental Working Papers 200224, Rutgers University, Department of Economics.
  9. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
  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. 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.
  12. 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.

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