Pricing And Optimal Reset Policy Of Reset Option In Jump-Diffusion Models

Option is a financial derivates product, which occurs from USA in the middle of seventies. In the past several decades, it has developed rapidly as an effective means for speculating and against risks. To attract investor, a lot of financial firms have been introducing some new options such as path-dependent options (Exotic Option), and reset option is a typical one. Reset option has been traded not only in many stock markets but also in counter markets around the world.In this dissertation, the pricing of reset option in jump-diffusion model is studied by means of mathematical tools such as martingale theory and stochastic analysis etc. The main results are as follows:1. Combines the factors of jump-diffusion (Poisson process jump), stochastic interest rate, continuous stock dividends-payment and continuous volatility, and obtains the pricing formula of conventional single-point reset option.2. Tries to innovate in the conventional single-point reset option, and gains the pricing formula of reset option with stochastic reset time.3. Introduces a kind of evolving calculation method Particle Swarm Optimization (PSO) to solve the optimal investment problem, and presents a PSO based optimal reset policy for reset option, which can provide decision support for investor. Finally, a typical simulation is carried out to illustrate the validity of the policy.