Option Pricing Method & Application Driven By Asymmetric Jump Diffusion Process

Option pricing is always one of cores of financial mathematics. Assumed that stock frustrates in the GBM, Black and Scholes testified the famous Black-Scholes formula through non-arbitrage method. According to the assumption, the price of stock is a continuous function of time for the GBM is a continuous random process. However, various events emerging in the stock market will lead the price of stock to jump up and down. But the option pricing models established before suppose that the relative jumping height of the stock price is p.d.f. The hypothesis is not consistent with the reality, because the relative jumping height of the stock price is related with the importance of information. This dissertation does some new research in this field. And it falls into four chapters:Chapter one briefly introduces the basic concepts of option and other relative notions. This part also simply analyzes the positive effects that the six factors will impose on the option price.Chapter two completely deduces formula of European option pricing from the B-S option pricing model. Some models are also made in this part on the basis of further assumptions.Chapter three proposes a new European option pricing model which is. driven by asymmetric jump diffusion process. Firstly, it focuses on demonstration and comparison of several common methods for pricing the option to show the advantages respectively. Secondly, it presents a more accurate model describing asymmetric jump- diffusion option pricing. In this section, first, the events in the market are divided into K kinds in terms of probabilities which attach to the different degrees of importance. Second, the way in which stock price jumps is categorized into up and down, because the extensions of fluctuation are usually asymmetric by stimulating and empirically analyzing the "volatility smile" phenomenon in the option market. Then, it obtains the accurate pricing formula of European call option through distribution of Pareto and Beta under the assumption that the relative height of jump has a relationship with the importance of information.Chapter four focuses on the real options. It briefly introduces applications of option in both investment decision and financial analysis of company.