DI-UMONS : Dépôt institutionnel de l’université de Mons

Recherche transversale
(titres de publication, de périodique et noms de colloque inclus)
2013-09-09 - Colloque/Présentation - communication orale - Anglais - 0 page(s)

Heuwelyckx Fabien , "On the Convergence of European Options in the Binomial Model" in PhD-Day (BMS), Bruxelles, Belgique, 2013

  • Codes CREF : Mathématiques (DI1100), Probabilités (DI1132)
  • Unités de recherche UMONS : Probabilité et statistique (S844)
  • Instituts UMONS : Institut de Recherche sur les Systèmes Complexes (Complexys)
  • Centres UMONS : Modélisation mathématique et informatique (CREMMI)
Texte intégral :

Abstract(s) :

(Anglais) In this talk we introduce the notion of vanilla and lookback options. After that, we recall how Cox, Ross and Rubinstein built lattices to obtain a price and we explain how Cheuk and Vorst adapted them to price easily the lookback options. We study the convergence of the price of European lookback options with floating strike with the Cox-Ross-Rubinstein model to its evaluation with the Black-Scholes model when the number of intervals increases. We show as expected that this convergence is of order 1/√n starting from the writing of the price using a double sum. To prove this and to obtain the precise value of coefficients in the asymptotic expansion of the price, we use a lemma obtained from the work of Uspensky.