On the American Option Value Near its Exercise Region

  • Etienne Chevalier
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 12)

American options valuation leads to solve an optimal stopping problem or a variational inequality. These two approaches involve the knowledge of a free boundary, boundary of the so-called exercise region. Numerical methods exist to solve this kind of problems but these methods are not very efficient in high dimension because some information on the free boundary is needed. To improve our knowledge of the value function near its exercise region, we give here a lower bound for the difference between the value function and the pay-off function near the free boundary. This result can be used, for instance, to get some estimation for the convergence rate of the Bermudean option exercise region to the American one.


Convergence Rate Variational Inequality Free Boundary Option Price American Option 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BP03]
    Bally V., Pagès G.: Error Analysis of the quantization algorithm for ob- stacle problems, Stochastic Processes and their Applications 106, 1-40. (2003)zbMATHMathSciNetGoogle Scholar
  2. [B84]
    Benssoussan A.: On the theory of option pricing, Acta Applicandae Mathematicae 2, 139-158. (1984)MathSciNetGoogle Scholar
  3. [BL82]
    Benssoussan A., Lions J.L.: Applications of variational Inequalities in Sto- chastic Control, North-Holland. (1982)Google Scholar
  4. [BG97]
    Broadie M., Glasserman P.: Pricing American-style securities using simu- lation, Journal of Economic Dynamics and Control 21, 1323-1352. (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. [CW90]
    Carverhill A. P., Webber N.: American options: theory and numerical analysis. In: Options: Recent Advances in Theory and Practice, Manchester Univ. Press. (1990)Google Scholar
  6. [C04]
    Chevalier E.: American options and free boundaries, University of Marne-la-Vallée (2004)Google Scholar
  7. [EK81]
    El Karoui N.: Les aspects probabilistes du contrôle stochastique, Lecture Notes in Mathematics 876, 72-238. Springer-Verlag. (1981)Google Scholar
  8. [F75]
    Friedman A.: Stochasic differential equations and applications, vol. 1, New York: Academic Press. (1975)Google Scholar
  9. [JLL90]
    Jaillet P., Lamberton D., Lapeyre B.: Variational inequalities and the pricing of American options, Acta Applicandae Mathematicae, 21, 263-289. (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  10. [K88]
    Karatzas I.: On the pricing of American options, Applied Math. Optimization 17, 37-60. (1988)zbMATHMathSciNetGoogle Scholar
  11. [L98]
    Lamberton D.: Error estimates for the binomial approximation of American put options, Annals of Applied Probability 8, 206-233. (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  12. [LS01]
    Longstaff F. A., Schwartz E. S.: Valuing American Options by Simulations: a Simple Least Squares Approach, Review of Financial Studies 14, 113- 147.(2001)CrossRefGoogle Scholar
  13. [V99]
    Villeneuve S.: Options américaines dans un modèle de Black-Scholes multidimensionnel, Thesis, Université de Marne-la-Vallée. (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Etienne Chevalier
    • 1
  1. 1.Laboratoire d'Analyse et Probabilité, Boulevard François MitterrandUniversité d'Evry Val d'EssonneEvry CedexFrance

Personalised recommendations