Pricing Options Under The Assumption Of Dividends Following Jump-Diffusion Process

This paper focuses on option pricing under the assumption of dividends following Jump-Diffusion process.Black-Scholes formula has become one of the most important conclusions about models of continuous time in finance. In order to fit the actual situation of finance markets better and to meet the needs of more investors, The conditions of Black-Scholes model for derivatives pricing are gradually relaxed. People usually assume that the underlying assets follow a diffusion type process, the most common is the geometric Brown motion (GBM), but the actual study conveyed that Geometric Brown's movement is not the ideal tool for describing stock price process. When the market is affected by significant information, usually a greater "jump" turns up. And people usually assume that there is no dividend or dividends are continuous, But in the real world, it is difficult to achieve continuous dividend payments, especially in China, many of the listed companies often pay dividends once every six months or a year. So, taking the discrete dividend payments in to account when price the options has important practical significance.In this paper, we assume the existence of stochastic dividends which follow a Jump-Diffusion process. According to the arbitrage pricing theory, we get the price expression of underlying asset. American options, European options, Asian options pricing are discussed and the according option pricing formulas are derived when the dividends follow a Jump-Diffusion process.