2013/02/28 by Fabien Heuwelyckx, FABIEN HEUWELYCKX
Decision Sciences · Economics, Econometrics and Finance · #Binomial (polynomial) #Binomial distribution #Binomial options pricing model #Capital Investment and Risk Analysis #Convergence (economics) #Lemma (botany) #Order (exchange) #Probability and Risk Models #Stochastic processes and financial applications #Term (time) #Value (mathematics) #q-fin.PR
paper · pdf · doi:10.1142/s0219024914500253
arxiv created 2013/10/09 · openalex publication_date 2014/06/01 · arxiv updated 2015/02/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper, 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 [Formula: see text]. 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 [Formula: see text] in the expansion of the error; we also obtain the value of the term in 1/n if the risk free interest rate is nonzero. This modelization will also allow us to determine the first term in the expansion of the delta.