Engineering Application of Time-changed Lévy Process to Capture Jumps in Stock Market

In financial engineering, volatility in the stock return processes is one of crucial factors when we deal with asset pricing and risk management. Besides the continuous part and the big jumps, there are a great amount of small jumps in stock prices. In this paper, under the continuous-time financial framework, we use the time-changed Lévy process with infinite activity and infinite variation to construct the SVNIG model, which can capture small jumps. This model can describe the continuous volatility component and the jump component simultaneously. MCMC approach is then employed to estimate parameters and identify latent variables. Using Hushen300 composite index in China and Hang Seng index in Hong Kong, the empirical results show that there are massive small jumps in both markets, and SVNIG model can describe jump behavior more accurately than other models.