Pricing Of Currency Options Based On Black-Scholes Models With Different Borrowing And Lending Rate

In recent years,financial derivatives developed rapidly.The problem of option pricing caused by importance attached to mathematicians and financial experts at home and abroad.To control the risk effectively,we must make proper assessment of financial derivatives.The pricing of financial derivatives is also the key of its reasonable existance and healthy development.Among the pricing of financial derivatives,option pricing is researched most extensively.It's because:(1) Option pricing is easier than the pricing of other financial derivatives;(2)Many derivatives can be expressed as the portfolio of some options;(3)The principles of financial derivatives are similar,so it's possible to find the way of pricing of general financial derivatives by option pricing.In 1973,Fisher Black and M.Scholcs published the article "The Pricing of options and Corporate Liabilities",in this article,they created famous Black-Scholes model which has singnificance of corss time,got the analytic expression of the pricing of European put and call option.R.Merton promoted their coclusion in the article "Theory of Rational Option pricing".These two articles laid the foundation of opiton pricing models.From then on,theories and practice research about option pricing developed rapidly.But in the derivation of Black-Scholes Formula,it's assumed that borrowing rate and lending rate are all the risk-free interest rate.So we can't see how borrowing rate had lending rate affect option price separately.In reality,borrowing rate and lending rate are usually different.In this article,we assume that borrowing rate is bigger than(or equals to) lending rate(the risk-free interest rate),and some parameters about the stocks(expected rate of return,volatility,bonus rate) all change over time.Under the assumption we use BSDE and non-linear Feynman-Kac formula to derive the pricing foumula of European put and call options,thereby we can find the effects borrowing rate and lending rate do to the options price separately,also we can get the put-call parity at the same time. Then wc will research pricing of European currnecy options basend on Black-Scholes models with different borrowing and lending rate.At last,we will do some parameters sensitivity analysis.This paper is divided into 6 chapters.Chapter 1 is mainly an introduction to the background of the problem and some related results of other people.In Chapter 2,we recall the classical Black-Scholes Model in which borrowing rate and lending rate all equals to the risk-free interest rate.In the following chapters,we begin to research the Black-Scholes Model with different borrowing and lending rate and use it to price European currency option.In Chapter 3,we set up the basic framework under which we consider the problem and introduce several lemmas which will be used later..Through the former preparations,in Chapter 4,we get the main conclusions of our problem.In Chapter 5,we research pricing of currency options based on Black-Scholes models with different borrowing and lending rate.In the last chapter,we will do some parameters sensitivity analysis.