Esscher Transform And Option Pricing

As the take-off of China’s economy, China’s financial sector is also booming with the reform further develops. The option which is one of the most important means in the financial market is also growing in China’s financial market. So the role it played in China’s financial markets is also without a doubt.There are many different ways to solve the option pricing problem, because of the martingale method is simple and convenient, using martingale methods to solve the problem of option pricing has been the focus of people’s research.The Esscher transform is a time-honored tool in actuarial science. Since1994, the Gerber-Shiu introduced the Esscher transform from the actuarial field to mathematical finance field, it is so widely used because of its simple method. He had introduced the Esscher martingale measure in the same year. Combining with the martingale method, we can solve a variety of option pricing problems.In this paper, we summarized a variety of methods based on the previous method of drawing, concluded the concept and proprieties of martingale in financial market, researched many option pricing models by ways of martingale method and Esscher transform, compared the above two cases with different mathematical models and get the better answer in these two ways. Finally, using the Esscher martingale measure and the martingale method, we get the explicit solutions of several special Levy process option pricing models.