Pricing Discrete Dividend-Paying Stock Options with the Stair Tree

Pricing options on discrete-dividend-paying stocks has traditionally been solved by assuming that the stock price minus the present value of dividends follows the lognormal diffusion. The same assumption is also popular in tree methods to avoid combinatorial explosion. This approach undervalues the option since the volatility of the underlying stock price is underestimated. Our paper does away with this assumption with a new recombining tree, the stair tree model. Option pricing is solved efficiently and without bias. Numerical examples verify the algorithm's superior performance to existing methods.