A Study On Option Pricing With A Kind Of Exchange Option And A Kind Of Stochastic Interest Rates

Option theory is one of the greatest findings in the area of the world'seconomics in the 20 century.Together with the portfolio selection theory,the capital asset pricing theory,the effectiveness theory of market and acting issue,it is regarded as one of the five theory modules in modern finance.Many scholars have done a great deal of researches on Black-Scholes model and obtained a lot of results which is instructive to financial practice.In this paper it has made main conclusions as follows:(1)Under the risk-neutral hypothesis , we construct the model of stock price which jump process is a kind of special renewal process and obtain European general exchange option pricing formula under this model by means of martingale method. At last, this paper list some special cases of this model and generalize the pricing model and hedging strategy.(2)Construct stochastic different equation of stock price whose process is driven by exponential Ornstein-Uhlenbeck process .Under the risk-neutral hypothesis, then the equivalent martingale measure is found by means of Girsanov theorem, we obtain the European option pricing on stocks whose price is driven by exponential Ornstein-Uhlenbeck process under stochastic interest rate ,and the factors affect the interest rate and the price of the stocks are correlative.