Pricing European Contingent Claims With Generalized Ornstein-Uhlenback Process

In nearly decades years ,the ration research in the finance arose more and more attention. People are sure to realise the importance of the mathematics method and mathematics idea in the ration research for the grobality finance storm in the 20 century 90'. Especially the finance derivate market develops rapidly and the finance derivate product emerge in endlessly ,the invest chances and the eluding-risk tool to the investors are extended.Along with acceding to WT0,we have to face the opportunities and challenges for the grobality of finance ,and all kinds of derivate securities will enter into our national finance market ,so we have to account for the pricing problem and the investment decision-making.This disquisition studies some pricing problem of the European contingent claims.For extending and innovating some conclusion ,we obtain the better or the significative results which are more easily for manipulation to the finance practice .In detail we have main conclusions in this paper as follows:1.The interest rate is volatile in practicality.which will affect the invest conduct and the option price, and the price of stock can obey the other stochastic process.Under Hull-White interest rate model and stock price driven by Ornstein-Uhlenback process ,the pricing problem on European stock option with continuous dividend and foreign currency option are discussed,the price of options will be gained by the martingale method,and also the effect of interest rate to the option price via the analysis of data compute.2.Assuming the interest rate and the stock price are both .driven by Ornstein-Uhlenback process, we consider the possibility that the contracts are stopped before expire dates and obtain the European option price formulas with stochastic life.Furthermore.the result is used to other European contingent claims.3.The price of the reload option is obtained in this financal market where the stock follows Exp-Ornstein-Uhlenback process and the interest rates are also driven by Ornstein-Uhlenback process with martingale and stochastic analysis approach.Furthermore, this result is extended to multi-reload date model.4. The generic insurance actuary method is reseached under the assumed condition thatthe interest rate is a certain function.But in this paper,we extend the insurance actuary method to the cases that the interest rate is stochastic and the stock price is driven by generalized Ornstein-Uhlenback process.We also obtain the pricing formulas of the European option and the exchange option .