In this short article, we describe the pricing of an American option (call or put) on a share which may pay continuous dividends, using a method described by Broadie & Detemple (1997) as ‘not very elegant’. The method is simply to build a look-up table of option prices, which thus splits the problem of pricing American option prices into three sub-problems:

1. (A) accurate calculation of the values in the table;

2. (B) storage of the table, and access to it;

3. (C) rapid calculation of prices for given parameter values.

The most important problems are clearly B and C; in principle, we may take as long as necessary to fill up the table, since this calculation is done off-line, once only. Any of the methods discussed elsewhere in this volume by Broadie & Detemple (1997) and by AitSahalia & Carr (1997) could be used to compute the values in the table. We used the binomial method with 5000 time steps using Black-Scholes in the last step, as recommended by Broadie & Detemple.

It is worth remarking that by computing and storing the table of values, we are able to calculate greeks, and the exercise boundary with relatively little extra cost; this is a valuable advantage of this inelegant approach.

To describe the storage problem, let us first state the parametrisation which we used.