The Pricing Study On European Options Driven By Lévy Process

AbsIn the financial field, option as an effective means of preventing risks and speculative arbitrage has been widely researched and developed rapidly, so the option pricing is always an important subject in financial mathematics. As the underlying assets of financial derivatives are generally described by Brown motion, but it is limited. While Lévy process applied in financial engineering becomes more extensive and effective, it can accurately describe some complex distribution characteristics, such as: peak, fat tail, biased and so on, and can also reflect some non-continuous property of underlying assets in the movement. Therefore, the application of Lévy process in the financial field, especially the research on option pricing, has very important theoretical significance and practical significance.This paper mainly studies the relationship between Lévy process and the option price in two aspects. On the one hand, the article discusses the European option pricing problem of the B-S model based on Esscher transform, and talks about the European option pricing problem driven by Lévy process; On the other hand the article uses the maximum likelihood method to research Empirical meaning of six kinds of model driven by Lévy process based on Hang Seng Index option price, and compares the fitting effect of the call option price under the six model. Therefore, Lévy process is important to the research for option pricing, and mathematics is a very powerful tool of financial research, In addition this paper shows that financial practices can promote the development of the mathematical theory constantly.