| The option pricing theory, embodying many of the core questions of financial theory, is one of the most important achievements in the modern financial theory. With the development of financial market, the original option has been unable to adapt to the development of the market. Many more new type options should be designed to adapt to the development of the market and priced in order to meet the demand for investors.In this paper, the stochastic process and martingale theory have been introduced first. Then I apply those knowledge to price for the new type reset options, whose underlying asset pricing obey jump-diffusion process model. The innovations in this paper are following:1. Being based on the tradition of reset option pricing, I modify the underlying asset model to accord with the more general market model. Then under the hypothesis that the market has no friction, I give the pricing formula of this reset option by applying the martingale transform method.2. Modifying the model of the traditional reset option, I design a new type reset option with higher value which is actually a special European option. Then under the hypothesis that the underlying asset pricing model obeys the jump-diffusion process model, I get the pricing formula of the new type option by using the measure transformation method.3. Being based on the pricing model of the existing geometric Asian-reset option, I modify the underlying asset pricing model to accord with the jump-diffusion process model. Then under the hypothesis that the market has no friction, I give the pricing formula of this new type option by applying the martingale transform method. |
