Some Kinds Of Pricing European Contingent Claims Under Vasicek Interest Rates Model

It is an important essay that studying the pricing of contingent claims is of theoretical significance and of practical value in financial mathematic. In the fields of the study of pricing of European contingent claims with interst rate being constant or deterministic functions, many authors have done many researchs and acquired a lot of achievements. However,when the interest rate being stochastic,these are not more.But the case about interest rate being stochastic exists in fact.So we must consider the random of interest rate affects the asset pricing. A complete and continuous market model which the process of asset price is assumed to be lognormal distribution arid the process of interest rate is assumed to be Vasicek are studied in this paper. By using Black-Scholes' risk-neutral valuation principal , pricing formulae of some European contingent claims are deduced .main results as follows:(1) The pricing formula of European call option and the put-call parity relation are deduced;(2)By using the above put-call parity relationship and the properties of conditional expectation, we also get the formula of as-you-like-it option under Vasicek model.(3)By applying the geometric average to compute the average price of assets which consists of two cases of continuous and discrete,the pricing formula for the Asian option of averag asset and average strike price and the parity relationship are obtained.