The Transform Analysis And Asset Pricing Research Based On The Affine Jump-Diffusion Process

As economic globalization goes deeper, the governments have to face the challenge to reduce the market volatility to realize a steady development. While the financial derivatives by virtue of its important role in avoiding risk, price discovery and value etc. and profound influence to the entire international financial market share position, play a decisive role in the current economic market. Therefore, in or der to reduce market volatility, derivatives is a very effective tool, as the product of one of the most important factors of pricing derivative product, has also become the focus of attention in today’s society, the study of the relationship between inter est rate and derivatives pricing has become more meaningful.Based on this significance, this paper introduces the domestic and foreign the current research situation about the term structure of interest rates and option pricing, and then proposes a tractable model of interest rate term structure, under the Lévy jump. In addition, In order to apply the research results to the pricing of derivatives, the paper also carried out the transform analysis, the extended transform analysis and higher-order extended transform analysis of the model, and obtain the exact solutions of them.The core part of this article is: in order to make a better trade-off between the model complexities and ease of analysis and calculation of the two, this paper particularly introduces a research result that has been proved to be easy to handle, that is the dynamic asset pricing model, namely the state vector X obeys the affine jump diffusion process(referred to as AJD). Based on this, in order to better simulate the actual situation of market volatility, this paper analyzes a series of research on the model and its transformation under Lévy jumps.