The binomial option pricing model: The trouble with dividends

We identify a problem in the widely used binomial option pricing model when it is used to value options on an asset paying continuous dividends. It does not value pairs of European spot and futures options consistently even though they are theoretically equivalent. The inconsistency arises from the way dividend yield is incorporated into the jumps and probabilities. In addition, the model also has the tendency to undervalue American options due to suboptimal early exercise decisions. While the lingering effect of this problem diminishes asymptotically, it is nonetheless a concern for someone just beginning to learn the model or in applications where the use of a sufficiently large binomial tree is not practical or economical. We propose a simple modification to solve the problem and demonstrate the effectiveness of the solution.