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The American straddle close to expiry

Boundary Value Problems volume 2006, Article number: 32835 (2006) Cite this article

Abstract

We address the pricing of American straddle options. We use a technique due to Kim (1990) to derive an expression involving integrals for the price of such an option close to expiry. We then evaluate this expression on the dual optimal exercise boundaries to obtain a set of integral equations for the location of these exercise boundaries, and solve these equations close to expiry.

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References

  1. Alobaidi G, Mallier R: Asymptotic analysis of American call options. International Journal of Mathematics and Mathematical Sciences 2001,27(3):177-188. 10.1155/S0161171201005701

    Article  MathSciNet  MATH  Google Scholar 

  2. Alobaidi G, Mallier R: Laplace transforms and the American straddle. Journal of Applied Mathematics 2002,2(3):121-129. 10.1155/S1110757X02110011

    Article  MathSciNet  MATH  Google Scholar 

  3. Barles G, Burdeau J, Romano M, Samsoen N: Critical stock price near expiration. Mathematical Finance 1995,5(2):77-95. 10.1111/j.1467-9965.1995.tb00103.x

    Article  MATH  Google Scholar 

  4. Barone-Adesi G, Elliot RJ: Free boundary problems in the valuation of securities. In Working Paper. University of Alberta, Alberta; 1989.

    Google Scholar 

  5. Black F, Scholes M: The pricing of options and corporate liabilities. Journal of Political Economy 1973, 81: 637-659. 10.1086/260062

    Article  MATH  Google Scholar 

  6. Carr P, Jarrow R, Myneni R: Alternative characterizations of the American put option. Mathematical Finance 1992,2(2):87-106. 10.1111/j.1467-9965.1992.tb00040.x

    Article  MATH  Google Scholar 

  7. Chesney M, Gibson R: State space symmetry and two-factor option pricing models. Advances in Futures and Options Research 1993, 8: 85-112.

    MathSciNet  Google Scholar 

  8. Dewynne JN, Howison SD, Rupf I, Wilmott P: Some mathematical results in the pricing of American options. European Journal of Applied Mathematics 1993,4(4):381-398.

    Article  MathSciNet  MATH  Google Scholar 

  9. Geske R, Johnson H: The American put option valued analytically. Journal of Finance 1984, 39: 1511-1524. 10.2307/2327741

    Article  Google Scholar 

  10. Huang J-Z, Subrahamanyan MG, Yu GG: Pricing and hedging American options: a recursive investigation method. The Review of Financial Studies 1998,9(1):277-300.

    Article  Google Scholar 

  11. Jacka SD: Optimal stopping and the American put. Mathematical Finance 1991,1(2):1-14. 10.1111/j.1467-9965.1991.tb00007.x

    Article  MathSciNet  MATH  Google Scholar 

  12. Jamshidian F: An analysis of American options. In Working Paper. Merrill Lynch Capital Markets, New York; 1989.

    Google Scholar 

  13. Ju N: Pricing by American option by approximating its early exercise boundary as a multipiece exponential function. Review of Financial Studies 1998,11(3):627-646. 10.1093/rfs/11.3.627

    Article  Google Scholar 

  14. Kholodnyi VA: A nonlinear partial differential equation for American options in the entire domain of the state variable. Nonlinear Analysis 1997,30(8):5059-5070. 10.1016/S0362-546X(97)00207-1

    Article  MathSciNet  MATH  Google Scholar 

  15. Kholodnyi VA, Price JF: Foreign Exchange Option Symmetry. World Scientific, New Jersey; 1998:xx+134.

    Book  MATH  Google Scholar 

  16. Kim IJ: The analytic valuation of American options. Review of Financial Studies 1990,3(4):547-572. 10.1093/rfs/3.4.547

    Article  Google Scholar 

  17. Kolodner II: Free boundary problem for the heat equation with applications to problems of change of phase. I. General method of solution. Communications on Pure and Applied Mathematics 1956, 9: 1-31. 10.1002/cpa.3160090102

    Article  MathSciNet  MATH  Google Scholar 

  18. Mallier R, Alobaidi G: The American put option close to expiry. Acta Mathematica Universitatis Comenianae. New Series 2004,73(2):161-174.

    MathSciNet  MATH  Google Scholar 

  19. McDonald R, Schroder M: A parity result for American options. Journal of Computational Finance 1998,1(3):5-13.

    Google Scholar 

  20. McKean Jr HP: Appendix: a free boundary problem for the heat equation arising from a problem in mathematical economics. Industrial Management Review 1965, 6: 32-29.

    Google Scholar 

  21. Merton RC: Theory of rational option pricing. Journal of Economic and Management Sciences 1973, 4: 141-183.

    MathSciNet  MATH  Google Scholar 

  22. Samuelson PA: Rational theory of warrant pricing. Industrial Management Review 1965, 6: 13-31.

    Google Scholar 

  23. Tao LN: The Cauchy-Stefan problem. Acta Mechanica 1982,45(1-2):49-64. 10.1007/BF01295570

    Article  MathSciNet  MATH  Google Scholar 

  24. van Moerbeke P: On optimal stopping and free boundary problems. Archive for Rational Mechanics and Analysis 1975/76,60(2):101-148.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, College of Arts and Sciences, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates

    Ghada Alobaidi

  2. Department of Applied Mathematics, University of Western Ontario, London, ON, Canada, N6A 5B7

    Roland Mallier

Authors
  1. Ghada Alobaidi
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  2. Roland Mallier
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Correspondence to Ghada Alobaidi.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Alobaidi, G., Mallier, R. The American straddle close to expiry. Bound Value Probl 2006, 32835 (2006). https://doi.org/10.1155/BVP/2006/32835

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  • DOI: https://doi.org/10.1155/BVP/2006/32835

Keywords

  • Differential Equation
  • Integral Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation