Option Pricing Model And Its Generalization

The theory and practice of derivative securities have been developed very fast in recent twenty years all over the world. Many mathematicians and financial economists pay more and more attention to the problems of option pricing. Pricing options rationally is the center of option transactions. It is because that transactions go on through comparing the real market prices with the true option values. Among all the pricing systems, the investigation of option pricing is most important. The reasons for this are: (1) Comparing with other derivative securities, option is easy to price. (2)Many derivative securities can be expressed as the form of option's portfolio. (3)The pricing principles are same to all sorts of derivative securities, so it is possible to find pricing theory of other derivative securities through the option methods. This paper discusses the problem of pricing European options written on stocks. Using the method of Black-Scholes option pricing, three extended option pricing formulas are established. Main result are: (1)A new derivation method of the option pricing with the model parameters are functions of time t is given. Compared with the original derivation method, this method makes a more clear understanding of the influence of the model parameters changing along with time on the option pricing. (2) Some new option pricing formulas are derived on condition that the model is jump-diffusion, the stock pays dividends and the stochastic interest rate are continuous or discontinuous.