The Empirical Research Of European Put Options And Pricing American Put Option With Dividends

In the study of options, the most innovative work goes to Black and Scholes, who derived famous Black-Scholes(B-S) option Pricing equation in1973[1]. After1973,many scholars did a great deal of work, including the studies of nonlinear B – S equation or the extensions of B – S equation which are more close to the real situation. The domestic research about option started later, most of the researchers are based on the B – S model(for example [2-6]).Based on the research results of domestic and foreign, in this paper, firstly we will use the market data of Hong Kong’s heng seng index options to test the classic(B-S) model, the main work goes to the analysis and calculation of the implied volatility and the actual volatility, as well as the calculation of the theoretical price and the actual price of the option. The experimental results verify that B- S model is efficient for market.Then we get the theoretical price of American put options about WMT and MCD stock by Crank- Nicolson difference scheme. Finally we will consider American put options with dividends which is in the form of variational inequality equation[7],we use the finite difference method to make the American put option with dividends pricing model discretize into difference equations, and obtain the explicit difference schemes. The numerical experiments verify that the finite difference schemes is efficient. On this basis, we propose the splitting method to solve American put options, and transform the American put option into a free boundary problem of ordinary differential equations. We solve the American option by using the free boundary and the connection conditions, and then we can acquire the mathematical expressions of pricing the American option with dividends.