A study of jump risks in asset prices : an investment perspective

Abstract

Significant jumps have been found in stock prices and stock indexes, which implied that jump risk is part of systematic risks. Since jump risk is priced, adding jump risk into the traditional finance models has significant empirical and theoretical meanings. Earlier attempts to model and estimate jumps are based on parametric jump-diffusion models. Due to the limitation of parametric models, the literature is rapidly moving towards using nonparametric methods to study various attributes of jumps in stock prices and the associated jump risks. Two nonparametric methods are employed to extract two different types of jump risks in this thesis. The Barndorff-Nielsen and Shephard (2006) method tests for large and rare jumps and can only be used to estimate the total jump risks. Macinni (2009) method allows for both small jumps with infinite activity and large jumps with finite activity. However, the latter method is computationally intensive and is only used to extract the systematic jump risks by applying it only to the market returns.

Jump estimations are computed on 1300 individual stocks and 1 index. Jump risks are found in all 1300 stocks and the index and jump risk is a small component of the total risk. SmallCap stocks tend to have higher diffusion and jump risks than MidCap and LargeCap stocks. When SmallCap stocks are used to form portfolio, its diversification gain is higher than that of portfolios formed by MidCap or LargeCap stocks. A portfolio's diffusion and jump risks decrease at a diminishing speed as the number of its constituents increase and its jump risk decreases faster than diffusion risk. However, the uncertainty associated with the diversification gain of jump risk is much higher than that of the diffusion risk. To measure the systematic diffusion and jump risks, CAPM is dichotomised into a two-factor model, two independent factors representing the diffusion and jump return processes. The diffusion and jump betas for the 1300 stocks are estimated. The diffusion and jump betas for stocks tend to be statistically different from each other.