Convergence rates of recombining trees for pricing options on stocks under GBM and regime-switching models with known cash dividends

• The convergence rates of the tree methods for fixed cash dividend GBM models are studied.
• A tree method for fixed cash dividend regime-switching models is designed.
• The convergence rates for fixed cash dividend regime-switching models are proved.
• Numerical examples are provided.

In the literature there appear various kinds of binomial trees for pricing options on stocks under geometric Brownian motions (GBMs) with known cash dividends. The aim of this paper is to compare the performance of the existing binomial trees in aspect of the convergence rates, which are usually used to measure precisely how fast the approximate values converge to the exact one, and to give a theoretical proof of the convergence rates for the interpolation binomial trees which are based on a model that excludes the arbitrage possibilities. Also the paper extends the studies to the regime-switching models with known cash dividend payment.