The Study On Pricing Of Alternative Options

In global financial markets,there are a lot of derivatives which are accompanied by derivatives is risk.If you want to effective management of risk,you will need to carry on the reasonable pricing of these derivatives,such as options,forwards,futures and swaps.Options is one of the most common financial derivatives.So,the option pricing problem is one of the core problems in financial mathematics.Asset managers use alternative options in the same market to get results in two types of assets compared the risk of lower profits,or get results in two markets of instituting risk and return.In this paper,we will study the pricing of the better-of-two call option and worst-of-two call option under the geometric Brownian motion,and revise the previous results,and make the sensitivity analysis of the option pricing formula with constant parameters.We study the pricing of the better-of-two call option and worst-of-two call option under parametric parameters,and consider the pricing of the better-of-two call option and worst-of-two call option based on the logarithmic rate of return under the jump diffusion model.The thesis consists of five parts.Introduction,the history and background and development status of option pricing and its research content and significance are introduced.In Chapter 1,the definition of Brownian motion,It(?)'s Lemma,Girsanov's Theorem,and other related lemmas and definitions are introduced.In Chapter 2,we consider the pricing formula of the better-of-two call option and worst-of-two call option based on the logarithmic rate of return under the constant parameters.Through measure transformation,we will transform the real world into a risky neutral world,and then get its analytical pricing formula through the derivation calculation.In this chapter,we will further discuss the Greek values of Theta and Rho,and made the sensitivity analysis to the option pricing formula with constant parameters to measure the specific risk of the option.We will use Matlab to graph,and obtain the relation curves between Theta and Rho and each value.In Chapter 3,in the financial markets,interest rate,volatility and other parameters are changed with time,in this chapter,we will obtain the pricing formula of the betterof-two call option and worst-of-two call option based on the logarithmic rate of return in the Time-varying parameters.In Chapter 4,there is always an occasional jump in asset prices,and volatility is irregular.In order to make asset prices model closer to reality,we will consider the pricing formula of the better-of-two call option and worst-of-two call option based on the logarithmic rate of return under the jump diffusion model.In Chapter 5,we summarize the main results obtained in this paper and propose the problems that need to be solved in the further.