Option Pricing Related Issues Discussed

"Option" is considered to be a successful example of pioneering practice in international finance market of the 20th Century. At the same time, it inserts the development of financial and banking theory with vigor and vitality. Although options have been traded in American Chicago Board Option Exchange since 1973, almost nobody could, at that time, foresee that they would bring about enormous pound and influence on practice and financial and banking theory in the following several decades. Now option market has become an important part of international finance market. Under such background, research and application of option pricing theory, currently, set off a new upsurge of inovation in the field of financial theory.By means of mathematical tools such as martingale theory and stochastic analysis, this paper shall mainly study many option pricing problems in financial economy, attempts to extend and innovate some of these conclusions, and try to obtain some better conclusions or the results which are easy to operate and instructive to financial practice.First, the paper summarize the origin, development, academic trend and research method of option pricing theory in chapter one. The basic models of option pricing are introduced in chapter two. Chapter three, four and five study option pricing with the underlying assets price obeying jump-diffusion processes. Chapter three extends the jump-diffusion model when events causing stock price to jump are classified into many kinds according to their importance. Chapter four develops the reload option pricing formula. Chapter five studies the option pricing of several underlying assets' maximum. Stochastic life option pricing problems are dealed with in chapter six, seven and eight, in which chapter six deals with option pricing with different borrowing and lending rate, chapter seven studies option pricing under the underlying assets obeying jump-diffusion processes, and chapter eight deals with two-dimensional option pricing under the underlying assets obeying jump-diffusion processes. Chapter nine, ten and eleven develop the discrete methods to price exotic options, in which chapter nine prices exotic options using the shooting target gird method, chapter ten prices the options using improved shooting target gird method when the underlying asset obeys CEV process, and chapter eleven prices the double lookback options using five-bifurcation tree method. In the last chapter, application of option pricing theory is studied in executive stock option plan.