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Evaluation of American Strangles

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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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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 83.

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Date of creation: 01 Jun 2002
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Handle: RePEc:uts:rpaper:83

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Keywords: american options; volterra integral equation; free-bondary problem;

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References

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  1. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
  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. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  4. 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.
  5. 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.
  6. Andrew Ziogas & Carl Chiarella, 2003. "McKean’s Method applied to American Call Options on Jump-Diffusion Processes," Computing in Economics and Finance 2003 39, Society for Computational Economics.
  7. 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.
  8. 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.
  9. Parkinson, Michael, 1977. "Option Pricing: The American Put," The Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January.
  10. 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.
  11. 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.
  12. Peter Carr & Robert Jarrow & Ravi Myneni, 1992. "Alternative Characterizations Of American Put Options," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 87-106.
  13. 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.
  14. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-72.
  15. 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.
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Cited by:
  1. Mahayni, Antje & Schoenmakers, John G.M., 2011. "Minimum return guarantees with fund switching rights—An optimal stopping problem," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1880-1897.
  2. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
  3. 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.
  4. 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.
  5. Anna Battauz & Marzia De Donno & Alessandro Sbuelz, 2013. "Real Options and American Derivatives: the Double Continuation Region," Working Papers 499, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  6. 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.
  7. Detemple, Jérôme & Emmerling, Thomas, 2009. "American chooser options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 128-153, January.

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