| Summary: | 碩士 === 國立高雄第一科技大學 === 金融研究所 === 102 === With the innovation of the derivatives, the S&P500 index as an underlying asset of the volatility index (VIX) introduced by the Chicago Board Options Exchange (CBOE) was adopted as the research object in this study.Since the financial crisis in 2008,the degree of market volatility has increased substantially. Also the situation of the random process has been found jumping in the VIX data.In addition to the Merton diffusion model(1974),the jump component was added in the study in which Merton (1976) jump diffusion model was also adopted. Besides, according to recent literature,in the stochastic process including jump component ,the phenomenon without convergence might occur by using maximum likelihood estimation (MLE) to estimate parameters. Therefore,to estimate jump component in the random process in the study,we adopted the method of the expectation maximization(EM) to estimate the parameters. We also compared all of the models in this paper to determine the best-fit model by using the Log-Likelihood value and tried to derive the VIX derivatives and to analyze the sensitivity of the derivatives in the random process based on the models we selected.
|
|---|
