Binomial models for option valuation - examining and improving convergence

Dietmar P. J. Leisen, Matthias Reimer
1996 Applied Mathematical Finance  
Binomial models, which rebuild the continuous setup in the limit, serve for approximative valuation of options, especially where formulas cannot be derived mathematically. E v en with the valuation of European call options distorting irregularitiesoccur. For this case, sources of convergencepatterns are explained. Furthermore, it is proved order of convergence one for the Cox{Ross{Rubinstein 79]model as well as for the tree parameter selections of Jarrow and Rudd 83], and Tian 93]. Then, we de
more » ... n 93]. Then, we de ne new binomial models, where the calculated option prices converge smoothly to the Black{Scholes solution and remarkably, w e e v en achieve order of convergence two w i t h m uch smaller initial error. Notably, solely the formulas to determine the constant up{ and down{factors change. Finally, all tree approaches are compared with respect to speed and accuracy calculating relative root{mean{squared error of approximative option values for a sample of randomly selected parameters across a set of re nements. Approximation of American type options with the new models exhibits order of convergence one but smaller initial error than previously existing binomial models.
doi:10.1080/13504869600000015 fatcat:3src7elozzhqxaas3ozqmhz22u