Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Analysis of the zigzag convergence for barrier options with binomial trees

Auteur(s):

Code(s) de Classification MSC:

• 65U05 Numerical methods in probability and statistics
• 60Hxx Stochastic analysis, see also {58G32}
• 35K20 Boundary value problems for second-order, parabolic equations
• 90Axx Mathematical economics, {For econometrics, see 62P20}

Résumé: In this paper, we analyze the rate of convergence of a standard binomial tree method to price European style single and double barrier options in a Black-Scholes setup, when the refinement of the tree $n$ goes to $+\infty$. We give a mathematical proof of the zigzag convergence observed numerically, by computing the main term in the approximation error. This enables us to correct the standard procedure to get more accurate prices. The method which we use to analyze the binomial approximation is quite generic and can be applied to study the convergence of other tree methods for pricing European style barrier options.

Mots Clés: binomial trees ; barrier options ; convergence rate ; parabolic PDE's

Date: 1999-10-07

Prépublication numéro: PMA-536

Fichié postscript : PMA-536.ps
(attention : contrairement au fichier PMA-536.ps, le fichier PMA-536.dvi lié au titre de cette fiche ne contient pas les figures qui accompagnent le texte).