Binomial algorithms for the evaluation of options on stocks with fixed per share dividends

Abstract

We consider options written on assets which pay cash dividends. Dividend payments have an effect on the value of options: high dividends imply lower call premia and higher put premia. Recently, Haug et al. [13] derived an integral representation formula that can be considered the exact solution to problems of evaluating both European and American call options and European put options. For American-style put options, early exercise may be optimal at any time prior to expiration, even in the absence of dividends. In this case, numerical techniques, such as lattice approaches, are required. Discrete dividends produce discrete shift in the tree; as a result, the tree is no longer reconnecting beyond any dividend date. While methods based on non-recombining trees give consistent results, they are computationally expensive. In this contribution, we analyse binomial algorithms for the evaluation of options written on stocks which pay discrete dividends and perform some empirical experiments, comparing the results in terms of accuracy and speed.