Recombining Binomial Tree for Pricing Options on Stocks with Known Dollar Dividends

Abstract

Known discrete dollar dividends lead to non-recombining binomial trees (NR-BT) with an explosion of nodes, which are more difficult to implement and much less efficient. This paper proposes a method for constructing a recombining binomial tree via balanced dividend adjustments (BDA). BDA splits the dividend linearly before and after the dividend payment, while modifying the stock price at every node and keeping the tree recombining. A heuristic proof shows that BDA appears to approximate its exact NR-BT extremely well. This is mostly confirmed by numerical results, with 31 out of 36 BDA pricing errors against NR-BT being less than 0.5% in absolute values for American options with up to two dividends.

Keywords: known dollar dividends; recombining binomial tree; balanced dividend adjustments; pricing American options; non-recombining binomial tree

JEL Classification: G13, G12