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Monte Carlo Valuation of American Options through Computation of the Optimal Exercise Frontier

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  • Ibáñez, Alfredo
  • Zapatero, Fernando

Abstract

This paper introduces a Monte Carlo simulation method for pricing multidimensional American options based on the computation of the optimal exercise frontier. We consider Bermudan options that can be exercised at a finite number of times and compute the optimal exercise frontier recursively. We show that for every date of possible exercise, any single point of the optimal exercise frontier is a fixed point of a simple algorithm. Once the frontier is computed, we use plain vanilla Monte Carlo simulation to price the option and obtain a low-biased estimator. We illustrate the method with applications to several types of options.

Suggested Citation

  • Ibáñez, Alfredo & Zapatero, Fernando, 2004. "Monte Carlo Valuation of American Options through Computation of the Optimal Exercise Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(02), pages 253-275, June.
  • Handle: RePEc:cup:jfinqa:v:39:y:2004:i:02:p:253-275_00
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    1. Oliver Musshoff & Norbert Hirschauer, 2008. "Investment planning under uncertainty and flexibility: the case of a purchasable sales contract ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 52(1), pages 17-36, March.
    2. Zhongkai Liu & Tao Pang, 2016. "An efficient grid lattice algorithm for pricing American-style options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 36-55.
    3. D. Andricopoulos, Ari & Widdicks, Martin & Newton, David P. & Duck, Peter W., 2007. "Extending quadrature methods to value multi-asset and complex path dependent options," Journal of Financial Economics, Elsevier, vol. 83(2), pages 471-499, February.
    4. Cartea, Álvaro & Williams, Thomas, 2008. "UK gas markets: The market price of risk and applications to multiple interruptible supply contracts," Energy Economics, Elsevier, vol. 30(3), pages 829-846, May.
    5. repec:eee:finlet:v:22:y:2017:i:c:p:233-243 is not listed on IDEAS
    6. Marcelo G. Figueroa, 2006. "Pricing Multiple Interruptible-Swing Contracts," Birkbeck Working Papers in Economics and Finance 0606, Birkbeck, Department of Economics, Mathematics & Statistics.
    7. Chockalingam, Arun & Muthuraman, Kumar, 2015. "An approximate moving boundary method for American option pricing," European Journal of Operational Research, Elsevier, vol. 240(2), pages 431-438.
    8. 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.
    9. repec:eee:forpol:v:85:y:2017:i:p1:p:76-84 is not listed on IDEAS
    10. Tubetov, Dulat & Musshoff, Oliver & Kellner, Ulla, 0. "Investments in Kazakhstani Dairy Farming: A Comparison of Classical Investment Theory and the Real Options Approach," Quarterly Journal of International Agriculture, Humboldt-Universität zu Berlin, vol. 51.
    11. Kovacevic, Raimund M. & Pflug, Georg Ch., 2014. "Electricity swing option pricing by stochastic bilevel optimization: A survey and new approaches," European Journal of Operational Research, Elsevier, vol. 237(2), pages 389-403.
    12. Alesii, Giuseppe, 2005. "VaR in real options analysis," Review of Financial Economics, Elsevier, vol. 14(3-4), pages 189-208.
    13. Carl Chiarella & Jonathan Ziveyi, 2014. "Pricing American options written on two underlying assets," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 409-426, March.
    14. Jain, Shashi & Roelofs, Ferry & Oosterlee, Cornelis W., 2013. "Valuing modular nuclear power plants in finite time decision horizon," Energy Economics, Elsevier, vol. 36(C), pages 625-636.
    15. Haverkamp, Matthias Wolbert & Musshoff, Oliver, 2013. "Are short rotation coppices an alternative to traditional agricultural land use in Germany? A real options approach," 2013 Conference (57th), February 5-8, 2013, Sydney, Australia 152184, Australian Agricultural and Resource Economics Society.
    16. Lars Stentoft, 2013. "American option pricing using simulation with an application to the GARCH model," Chapters,in: Handbook of Research Methods and Applications in Empirical Finance, chapter 5, pages 114-147 Edward Elgar Publishing.
    17. Bender Christian & Kolodko Anastasia & Schoenmakers John, 2006. "Policy iteration for american options: overview," Monte Carlo Methods and Applications, De Gruyter, vol. 12(5), pages 347-362, November.
    18. 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.

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