Some Issues About The Pricing Of Contingent Claim Under Stochastic Interest Rate

There are four parts in this paper. The first chapter introduce the development of financial mathematics, Backward Stochastic Differential Equation (BSDE) and the pricing of contingent claim, especially of European style by using the method of BSDE.In Chapter two, the contingent claim pricing of portfolio is discussed under the situation that the interest rate is stochastic and stocks are not independent at all. The stocks declare dividends and there is only one interest rate in the securities market. And European & Asian options are both conserved in the hedge of portfolio.The European contingent claim pricing is analyzed in the third part on the condition of loan interest rate higher than the deposit one together with both stochastic. And the optimal invest strategy is also obtained.In the last part, the emphasis is put on the pricing of exchange rate when the interest rate is stochastic. The formula of exchange rate is described through the transfer of the prices of the two kind zero-coupon bonds shared by native country and foreign country with respect to the exchange rate. Then the pricing of exchange rate can be derived under the definition of European option, In addition, the three price processes of exchange rate, foreign bond and native bond are not independent.