The Study Of Reload Option And General Exchange Option Pricing

Generally on the options pricing are subject to the assumption that the stock pricefor the continuous di?usion process [1], but when actually analyze stock price behaviorprocess, they discovered that the stock price is not continuous. So reference [2] proposedthe stock price obeys jump-di?usion model, for reload option, reference [3] gives thesolution of which the stock price obeys continuous di?usion process. Reference [4] loadedthe pricing formula which the reload option follows the jump-di?usion process and thevarious parameters are the constant, however, each kind of parameter is the constant isnot realistic. In this paper, considering the various parameters are not the constant, thepricing formula of reload option and general exchange option are given which obey thejump-di?usion process by taking advantage of numeraire transformation, martingale, andother random analysis mathematical tools.The article is divided into three chapters, Chapter I Survey, given the history anddevelopment of options and the results of their predecessors.Chapter II is mainly in the di?usion of models with reload option(only consider thesituation once again loaded), given its pricing formula (theorem 2.1 and corollary 2.1).Chapter III is to jump-di?usion model with reload option(only consider the situationonce again loaded), given its pricing formula (theorem 3.1 and corollary 3.1 ).Chapter IV mainly in the jump-di?usion model to study general exchange option,presents its pricing formula (theorem 4.1 and corollary 4.1 ).In Appendix, we list the theory of numeraire transformation and some of the basicconcepts such as It?o integral, Brown motion and so on.