Researching In Several Types Of European Option Pricing Involving Transaction Costs And Dividends

Contingent claims pricing is one of the core problems in financial mathematics. Itinvolves many fields of the modern financial mathematics, such as asset pricing theory,portfolio theory, stochastic analysis in mathematics as well as optimization theory andother disciplines. To effective forecast and management the risks, we need to appraisaland evaluation the financial derivative securities correctly. How to determine a fairprice of financial derivatives securities fast and effectively, is the key of their reasonableexistence and health development.This paper mainly discusses the related issues of European option pricing. Based onthe transaction costs and dividends, thinking that Underlying Assets is subject to themixing process, we gain the option pricing equation whose underlying asset to obey themixing process, rainbow option pricing equation and multi factor option pricing equation,and the binomial tree model and the matrix algorithm of European option.First, by changing the basic assumptions of Black-Scholes option pricing model, westudy European option pricing with transaction cost and dividend. thinking thatUnderlying asset satisfied mixed process and using the way of portfolio simulationoptions income, the option pricing equation of option price about underlying assetsatisfied mixed process with transaction costs and dividends is obtained. And we deducethe European option pricing model about underlying asset satisfied mixed process withtransaction costs and dividends. At the same time, rainbow option pricing equation aboutunderlying asset satisfied mixed process with transaction costs and dividends is obtained.Multi factor option pricing equation is also obtained.Second,on the definition of considering transaction costs and dividends, we consider binomial tree diagram of European option with dividend and transaction cost. From theknown red interest rates and transaction costs, and the known bonus amount andtransaction costs amount two aspects, the European option of binomial tree model isgiven; According to the following two kinds of circumstances are discussed, Separatelyaccording to the known red interest rates to pay dividends and the fixed proportion ofturnover to charge transaction cost, and according to the known bonus amount to paydividends and Transaction costs amount to charge transaction cost, the matrix algorithmof binomial tree model of European option is obtained.