Fast Trees for Options with Discrete Dividends

Abstract

The valuation of options using a binomial non-recombining tree with discrete dividends can be intricate. This paper proposes three different enhancements that can be used alone or combined to value American options with discrete dividends using a non-recombining binomial tree. These methods are compared in terms of both speed and accuracy with a large sample of options with one to four discrete dividends. This comparison shows that the best results can be achieved by the simultaneous use of the three enhancements. These enhancements when used together result in significant speed/accuracy gains in the order of up to 200 times for call options and 50 times for put options. These techniques allow the use of a non-recombining binomial tree with very good accuracy for valuing options with up to four discrete dividends in a timely manner.