Based On Jump - Diffusion Process Of Determination Of The Optimal Hedging Ratio

With development of research on times series of financial assets prices or their returns, increasing numbers of studies’results show that those time series are not smooth but with jumps of different scales which making the time series incontinuous. There are many reasons causing those jumps with most important one being that information of great importance and impact arrives at the market. Although jumps occur infrequently, their influence can’t be ignored for their scales are big. Therefore, we need to incorporate jump-diffusion process in the model to better describe the big changes in prices or returns. Big change in times series of financial assets prices or their returns also can’t be neglected in the study of hedging with futures market for infrequent big jump will bring big change to the hedging portfolios, which is not expected by the hedgers.In this paper, firstly, I summed up the development on hedging theory, from covering all or most of the risks to portfolio theory and from "transfer of risks" to "managing of risks", and also introduced hedging methods under different hedging aims with emphases on time-varying hedging ratio theory. Secondly, I summarized the research and its development on the distribution and volatility of the time series of financial assets prices or their returns with highlight on character of leptokurtosis and fat-tail and such correspondent characters in volatility as volatility clustering, leverage effects and long memory of volatility. Also the research on jump-diffusion process was also introduced in this part. Thirdly, I gave detailed introduction of stochastic volatility (SV) model and developed SV models incorporated with jumps and also correspondent parameters estimation method—MCMC method under Bayesian theory.Based on better understanding of related theories and models, I made a study on China’s cash and futures copper and aluminum markets with findings as follows:the SVCJ model which incorporated correlated jumps in return and volatility is better than SV model which hasn’t included jumps and SVJ model with only jumps in returns. And in the research on the optimal hedging ratio and their correspondent efficiency under above-mentioned three models, I got the results that in SVCJ model the variance of return of hedging portfolio decreased most than in the other two models and that the mean of return of hedging portfolio also decreased quicker than in the other two models.Although jumps-diffusion process already incorporated in the study, I only considered correlated jumps in return and volatility and jumps in return. And jumps in return and volatility can be independent, which should be taking into account in future research.