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A Survey of the Integral Representation of American Option Prices

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Abstract

This paper surveys some of the literature on American option pricing, in particular the representations of McKean (1965), Kim (1990) and Carr, Jarrow and Myneni (1992). It is proposed that the approach regarding the problem as a free boundary value problem, and solving this via incomplete Fourier transforms, is the most robust for further developments involving more complex payo structures, and higher dimensional problems such as multi-asset American options. Some comparison of di erent numerical solution methods is also provided.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp118.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 118.

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Date of creation: 01 Feb 2004
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Handle: RePEc:uts:rpaper:118

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Keywords: American options; Volterra integral equation; incomplete Fourier transform; free-boundary problem;

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  1. Peter Carr & Robert Jarrow & Ravi Myneni, 1992. "Alternative Characterizations Of American Put Options," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 87-106.
  2. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-62, May.
  3. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 31-62, January.
  4. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
  5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  6. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
  7. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-72.
  8. Parkinson, Michael, 1977. "Option Pricing: The American Put," The Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January.
  9. Chiarella, Carl & El-Hassan, Nadima & Kucera, Adam, 1999. "Evaluation of American option prices in a path integral framework using Fourier-Hermite series expansions," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1387-1424, September.
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Cited by:
  1. Carl Chiarella & Andrew Ziogas, 2006. "American Call Options on Jump-Diffusion Processes: A Fourier Transform Approach," Research Paper Series 174, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Carl Chiarella & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2005. "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton with Jumps," Research Paper Series 167, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Carl Chiarella & Andrew Ziogas, 2002. "Evaluation of American Strangles," Research Paper Series 83, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Pierangelo Ciurlia & Ilir Roko, 2005. "Valuation of American Continuous-Installment Options," Computational Economics, Society for Computational Economics, vol. 25(1), pages 143-165, February.
  5. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlogl, 2007. "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 365-399.

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