Option Pricing Model And Its Generalization

Morden finance theory is consummating and maturing with the continuously development of finance market. All sorts of financial derivatives are appearing. In the latest decades, the development of financial derivatives has becoming one of the most inprotant factors influenceing the global economy. Especially for the option, it has the functions in venture evading, venture investment and value detection etc. It has the properties of agility and diversity as well. Therefore, since the 1990s, it has become one of the most energetic financial derivatives and has been applied broadly and rapidly.We know that Black-Scholes option pricing model is constructed based on the following hypothesis: in the period of validity, the ratio of interest without venture and fluctuating ratio of finacial asset is invariable. But the realistic situation is not in such case. Because fluctuating ratio is affected by lots of uncertain factors, the fluctuating ratio is always one variable and it changes randomly and has no aftereffect, we suppose that it obeys Markov process. It is the same for fluctuating ratio. In this thesis, based on the existing foundation, we did the following discussions in several cases: (1) Option pricing model in which the ratio of interest is unchanged and fluctuating ratio obeys continuous time, discrete, finite and homogeneous state Markov process; (2) Option pricing model in which the ratio of interest is unchanged and fluctuating ratio obeys continuous time, discrete, countable and homogeneous state Markov chain; (3) Option pricing model in which the ratio of interest and fluctuating ratio obeys discrete time, discrete, finite and homogeneous state Markov chain.