Pricing The Options In The Financial Market Driven By The Jump Process

In recent years, with the vigorous development of the financial market, the theory for the option pricing has became the research focus of the mathematical finance. Because of the good function of risk-averse, risky investment, value discovery and characteristics of flexibility and diversity, it has become the most important part of the financial theory. Hence its pricing theory is very important for the academic, Exchange and OTC.This paper is mainly about pricing the options in the market driven by the jump process. The main contexts for the paper are as follows:For pricing the contingent claims in the complex financial market, the underlying asset price process has been expanded from the general geometric Brownian motion to a type of jump-diffusion model-Poison process then to the more complex jump process-Levy process by the researchers, simultaneously they find the impact of important events happened in the past on the current asset price, that is to say a certain time delay. Based on the results of Corcuera, JM., Nualart, D. and so on, in the first part of the paper, we price the contingent claim when the underlying asset follows a combination model of a time delay and the Levy process.For a new type of exotic options-Asian option,there are different forms. For different forms, the subjects of the researcher also differ a lot. Based on the jump-diffusion model,in the second part of the paper, we price the continuous geometric average Asian option when the price of the underlying assets follows a jump-diffusion model and then give the put-call formula.