The Option Pricing Model Based On The Jump-Diffusion

The option pricing theory has always been the core issue of the modern finance area. With the development of the global economy, the impact of the major events was evidently, and simply reply on the traditional B-S model would cause the investors to estimate the error expected. In response to this phenomenon, we assume that the major events would caused the underlying asserts jump in the life of the option. So we add the "jump" factor into the "diffusion" process, in order to make the model more closed to the actual.This thesis mainly includes the following contents:Part Ⅰ:improve the payment way to established the power jump-diffusion option pricing model, consider n types of assets, and this process was required to pay dividends through the process. In that way we established a new measure space, deduced the European call and put option pricing formula.Part Ⅱ:this thesis discuss the double exponential jump-diffusion option pricing model, we proposed the jump binary tree model use the Δ-hedge theory, and that the binary tree model to simplified the continuous model, at last we proved that under certain conditions the binary tree method would converge the continuous model.Part Ⅲ:analysis the different underlying assets’different effects, and induce a new model about the bond portfolio, at last analyzed the volatility effect of option pricing and use the inverse matrix to simply the model above.