Convergence of European Lookback Options with Floating Strike in the Binomial Model

Abstract: In this article we study the convergence of a European lookback option with floating strike evaluated with the binomial model of Cox-Ross-Rubinstein to its evaluation with the Black-Scholes model. We do the same for its delta. We confirm that these convergences are of order 1/Sqrt(n). For this, we use the binomial model of Cheuk-Vorst which allows us to write the price of the option using a double sum. Based on an improvement of a lemma of Lin-Palmer, we are able to give the precise value of the term in 1/Sqrt(n) in the expansion of the error; we also obtain the value of the term in 1/n if the risk free interest rate is non zero. This modelisation will also allow us to determine the first term in the expansion of the delta.