Discrete Dividend Payments Under The Option Pricing

Options are one of the most important tools of financial derivations.The core problem of options is options pricing. In recent years, in order to press close to the reality in financial market and satisfy more investors, researchers relaxed the hypothesizes for the B-S model. For example, it is necessary to study the pricing of options on stocks with dividends in reality, many papers considered the models with continuous dividends to simply the model. But in reality, the dividends paid continuously are hard. In China, the phenomena are obvious some listed companies may not pay dividends in many years. So it is important to study the pricing of options on stocks with discrete dividends in reality.For these reasons, this paper studies the pricing of the American put option on stocks with discrete dividends and the American look-back option by the finite-difference method. We give the explicit solution of option price with the discrete dividends and the float exercise price.