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A Survey of the Integral Representation of American Option Prices

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Author Info
Carl Chiarella () (School of Finance and Economics, University of Technology, Sydney)
Adam Kucera
Andrew Ziogas () (School of Finance and Economics, University of Technology, Sydney)

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

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Parkinson, Michael, 1977. "Option Pricing: The American Put," Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January. [Downloadable!] (restricted)
  3. Carl Chiarella & Andrew Ziogas, 2002. "Evaluation of American Strangles," Research Paper Series 83, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  4. 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. [Downloadable!] (restricted)
  5. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 547-72. [Downloadable!] (restricted)
  6. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  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. [Downloadable!]
  2. Pierangelo Ciurlia & Ilir Roko, 2004. "Valuation of American Continuous-Installment Options," Computing in Economics and Finance 2004 345, Society for Computational Economics. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!]
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