Pricing Of Several European Options Under Stochastic Interest Rates

Fisher Black & Myron Scholes's seminal paper " The Pricing of options and corporate liabilities " published in 1973 marks the beginning of financial derivative pricing theory.Since then,the study of financial derivative pricing theory has been full of vitality and reaped rich achievements.These researches are based on application to the mature securities market in the West.The securities market in our country is young and is a rising market.It is quite different from the mature market in many aspects,and also researches of the financial derivative pricing theory and application fall behind the West.It is very important and significance to use the financial derivative pricing theories in the West for reference and to strengthen the researches on financial derivative pricing theory and application in our securities market.In introduction,the conception of the option and the history of the option pricing theory are introduced.In the famous Black-Scholes model, it is assumed that the stock price is affectde by a stochastic factor,and obeys logarithm normal distribution,riskless interest rate and yield and fluctuate rate of stock price is all constant, and stock no pay dividend.But in actual financial market,the stock prices maybe affected by multi-factor,it pays dividend,and and riskless interest rate etc is function of time.In Chapter 2,first,it is supposed that basic asset-stock price is affected by some stochastic factor,it sastisfy to Ito stochastic differential equation,stock pay dividend, and riskless interest rate and dividend rate are function of time,the financial derivative market model is considered in the case when interest rate is stochastic.The pricing formulas of Bi-direction European option,Capped Calls, Deductible Calls, Innovative Reset Put Option and Innovative Reset Bear Market Warrants are deduced.In Chapter 3,it is assumed that the interest rate is a stochastic process and the volality of the price of the underlying assets follows a Marvov process, the pricing formula of the European call option under the stochastic interest rate and the volality of the price of the underlying assets follows a Marvov process are derived on the base of considering comprehensively the price action characters of the basic variables -bond and stock.In Chapter 4, the main results of this dissertation are summarized and some issues remaining unsolved are introduced.