A Study On Several Exotic Options Pricing Under Jump-diffusion Model

Option is financial derivates product, which occured from USA in the middle of seventies. In the past two decades, it has developed rapidly as an effective means for against risks and speculating. A lot of financial firms have introduced some new type of options to satisfy more investors require. How to pricing these exotic options is one of the kernel problems for financial and mathematics people.By means of mathematical tools such as stochastic process martingale theory and stochastic analysis, this dissertation construct mathematics model of stock with continous dividend and which price jump process is Poisson process and the height of jump abide by lognormal distribution. Under the model we by means of measure changes and martingale method and simply mathematical induce. The contents in this dissertation are as followers: 1. the dissertation induce four types of compound option pricing formula by taking call option on call option as example.2. This dissertation derived European reload option pricing formula prior to the due date only reloaded once again. 3. At the basis of traditional reset options this dissertation will derive a new type of reset options, and induce traditional reset option and the improved reset option-pricing formulas, and compare the traditional reset options, improved reset options, and standards European Option with value .