Based on the DF structure models for option pricing (Dai and Qin, 2005), this paper further discusses the DF structure models for three cases, i.e., when the underlying stock is dividend-paid, or when it is capital-split and when it is both dividend-paid as well as capital-split. These three cases are discussed separately, and then integrated in the general models for call and put options. Finally, examples are considered to compare the options prices calculated by the DF formulas and Black-Scholes formulas, and it is infered, that the DF formulas are better than the Black-Scholes formulas. It is also stated that DF formula is useful to traders in the financial market, as it can be conveniently adjusted according to the trading time.

With introduction of options trading of important derivative products, the researchers and investors have been paying increasing attention to the price of the options, especially the American put option. Studies on option pricing has yielded many significant results (Black and Scholes, 1973; Merton, 1976; Sharpe, 1978), and approximation methods for American put option (Johnson, 1983; Geske and Johnson, 1984; MacMillan, 1986; and Stapleton and Subrahmanyam, 1997). No exact analytic formula for valuation of an American put option was developed until 2005. The first structure model for options pricing was given by Dai and Qin in 2005. It can be used to determine the price of any options, including American put option. A recent problem faced is regarding the pricing of options (including the European and American call or put options) after the process of dividend-paying and capital-splitting on its underlings.

Based on the DF structure model for options pricing, this paper provides methods to price the options after the dividend-paying and capital-splitting on its underlings have been implemented. Finally, some empirical examples are considered which establishes the suitability of the models presented in this paper, to price the options on dividend-paying and capital-splitting stocks. These models are found to be very convenient in application.

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