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

Stocks frequently pay dividends, which has implications for the value of options written on these assets. High dividends imply lower call premia and higher put premia. Recently, Haug et al. [13] derive 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 it may be optimal to exercise 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, since at each node at an ex-dividend date and up to maturity a new binomial tree has to be generated and evaluated. In this contribution, we analyze binomial algorithms for the evaluation of options written on stocks which pay discrete dividends of both European and American type. We consider both algorithms which force the reconnection of the binomial tree, without altering the structure of the dynamics of prices, and an algorithm which translates a continuous efficient approximation.