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Evaluation of American Strangles

This paper presents a generalisation of McKean's free boundary value problem for American options by considering an American strangle position, where the early exercise of one side of the payoff will knock-out the out-of-the-money side. When attempting to evaluate the price of this American strangle, it is not correct to simply price the component American call and put options which make up the strangle, and take the sum of their values. The Fourier transform technique is used to derive the integral equation for the price of our American strangle. From this expression, a coupled integral equation system for the strangle's call- and put-side free boundaries is found. While the equation for the price of the strangle is simply the sum of its component American call and put option equations, the free boundary for each side is shown to have a more complex nature. Anumerical algorithm for solving the coupled integral equation system for the free boundaries is provided, and the resulting approximations are used to determine the price of the American strangle position. Numerical comparisons between the strangle price and the price of a portfolio formed from a long position in both an American call an American put option are presented.

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File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp83.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 83.

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Length: 50 pages
Date of creation: 01 Jun 2002
Date of revision:
Publication status: Published as: Chiarella, C. and Zigos, A., 2005, "Evaluation of American Strangles", Journal of Economic Dynamics and Control, 29(1-2), 31-62.
Handle: RePEc:uts:rpaper:83
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  1. Parkinson, Michael, 1977. "Option Pricing: The American Put," The Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January.
  2. 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.
  3. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-72.
  4. Peter Carr & Robert Jarrow & Ravi Myneni, 1992. "Alternative Characterizations Of American Put Options," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 87-106.
  5. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
  6. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  7. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 627-46.
  8. 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.
  9. Broadie, Mark & Detemple, Jerome, 1995. "American Capped Call Options on Dividend-Paying Assets," Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 161-91.
  10. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June.
  11. Carl Chiarella & Andrew Ziogas, 2004. "McKean's Methods Applied to American Call Options on Jump-Diffusion Processes," Research Paper Series 117, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. Ho, T S & Stapleton, Richard C & Subrahmanyam, Marti G, 1997. " The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique," Journal of Finance, American Finance Association, vol. 52(2), pages 827-40, June.
  13. 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.
  14. Huang, Jing-zhi & Subrahmanyam, Marti G & Yu, G George, 1996. "Pricing and Hedging American Options: A Recursive Integration Method," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 277-300.
  15. Carl Chiarella & Adam Kucera & Andrew Ziogas, 2004. "A Survey of the Integral Representation of American Option Prices," Research Paper Series 118, Quantitative Finance Research Centre, University of Technology, Sydney.
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