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  • Research Article
  • Open Access

The American straddle close to expiry

Boundary Value Problems20062006:32835

  • Received: 23 August 2005
  • Accepted: 22 March 2006
  • Published:


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.


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


Authors’ Affiliations

Department of Mathematics and Statistics, College of Arts and Sciences, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates
Department of Applied Mathematics, University of Western Ontario, London, ON, Canada, N6A 5B7


  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/S0161171201005701MathSciNetView ArticleMATHGoogle Scholar
  2. Alobaidi G, Mallier R: Laplace transforms and the American straddle. Journal of Applied Mathematics 2002,2(3):121-129. 10.1155/S1110757X02110011MathSciNetView ArticleMATHGoogle 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.xView ArticleMATHGoogle 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. 10.1086/260062View ArticleMATHGoogle 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.xView ArticleMATHGoogle 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.MathSciNetGoogle 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.MathSciNetView ArticleMATHGoogle Scholar
  9. Geske R, Johnson H: The American put option valued analytically. Journal of Finance 1984, 39: 1511-1524. 10.2307/2327741View ArticleGoogle 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.View ArticleGoogle Scholar
  11. Jacka SD: Optimal stopping and the American put. Mathematical Finance 1991,1(2):1-14. 10.1111/j.1467-9965.1991.tb00007.xMathSciNetView ArticleMATHGoogle 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/11.3.627View ArticleGoogle 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)00207-1MathSciNetView ArticleMATHGoogle Scholar
  15. Kholodnyi VA, Price JF: Foreign Exchange Option Symmetry. World Scientific, New Jersey; 1998:xx+134.View ArticleMATHGoogle Scholar
  16. Kim IJ: The analytic valuation of American options. Review of Financial Studies 1990,3(4):547-572. 10.1093/rfs/3.4.547View ArticleGoogle 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.3160090102MathSciNetView ArticleMATHGoogle Scholar
  18. Mallier R, Alobaidi G: The American put option close to expiry. Acta Mathematica Universitatis Comenianae. New Series 2004,73(2):161-174.MathSciNetMATHGoogle 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.MathSciNetMATHGoogle 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/BF01295570MathSciNetView ArticleMATHGoogle Scholar
  24. van Moerbeke P: On optimal stopping and free boundary problems. Archive for Rational Mechanics and Analysis 1975/76,60(2):101-148.MathSciNetView ArticleMATHGoogle Scholar


© Alobaidi and Mallier 2006

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