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Analytical Valuation of American-Style Asian Options

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Author Info

  • Asbjørn T. Hansen

    ()
    (Global Equities, Dresdner Kleinwort Benson, 20 Fenchurch Street, London EC3P 3DB, United Kingdom)

  • Peter Løchte Jørgensen

    ()
    (Department of Management, University of Aarhus, Building 350, DK-8000 Aarhus C, Denmark)

Abstract

This article derives the first analytical pricing formulas for American-style Asian options of the so-called floating strike type. Geometric as well as arithmetic averaging is considered. The setup is a standard Black-Scholes framework where the price of the underlying security evolves according to a geometric Brownian motion. A decomposition result that splits up the value of the floating strike American option into the price of an otherwise equivalent European option and an early exercise premium is first presented. This decomposition result is then manipulated further for the two separate types of averaging. With geometric averaging we derive an exact pricing formula, whereas with arithmetic averaging we develop an analytical approximation formula that proves to be very precise. Numerical examples are provided.

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File URL: http://dx.doi.org/10.1287/mnsc.46.8.1116.12027
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 46 (2000)
Issue (Month): 8 (August)
Pages: 1116-1136

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Handle: RePEc:inm:ormnsc:v:46:y:2000:i:8:p:1116-1136

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Related research

Keywords: asian options; american options; analytical valuation formulas; numerical work; change of numeraire;

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Cited by:
  1. Alfredo Ibáñez, 2003. "Robust Pricing of the American Put Option: A Note on Richardson Extrapolation and the Early Exercise Premium," Management Science, INFORMS, vol. 49(9), pages 1210-1228, September.
  2. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian options," Economics Working Papers 680, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Tomas Bokes & Daniel Sevcovic, 2009. "Early exercise boundary for American type of floating strike Asian option and its numerical approximation," Papers 0912.1321, arXiv.org.
  4. Andrea, Pascucci, 2007. "Free boundary and optimal stopping problems for American Asian options," MPRA Paper 4766, University Library of Munich, Germany.
  5. Marti G. Subrahmanyam & Bin Gao & Jing-zhi Huang, 1998. "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-067, New York University, Leonard N. Stern School of Business-.
  6. Tomas Bokes, 2010. "A unified approach to determining the early exercise boundary position at expiry for American style of general class of derivatives," Papers 1012.0348, arXiv.org, revised Mar 2011.
  7. Løchte Jørgensen, Peter, 2006. "Lognormal Approximation of Complex Pathdependent Pension Scheme Payoffs," Working Papers 2006-9, Copenhagen Business School, Department of Finance.
  8. Fard, Farzad Alavi & Siu, Tak Kuen, 2013. "Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 712-721.
  9. B. Gao J. Huang, . "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-002, New York University, Leonard N. Stern School of Business-.
  10. Bernard, Carole & MacKay, Anne & Muehlbeyer, Max, 2014. "Optimal surrender policy for variable annuity guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 116-128.
  11. Siu, Tak Kuen, 2005. "Fair valuation of participating policies with surrender options and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 533-552, December.

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