Jump activity analysis for affine jump-diffusion models: Evidence from the commodity market

This study performs a joint analysis of jump activity for commodities and their respective volatility indexes; it also compares the results thereof to those for equities. Exploiting a property of affine jump-diffusion models (i.e., that a volatility index quoted on the market is an affine function of the instantaneous volatility state variable), we perform a test of common jumps for multidimensional processes to assess whether an asset and its volatility jump together. Applying this test to the crude oil pair USO/OVX, the gold pair GLD/GVZ, the S&P500/VIX, and three stock/volatility index pairs, we find strong evidence that these assets and their respective volatility indexes do not jump together. However, a copula analysis shows that for the equity index and individual stocks, there is a dependency between the jump sizes in the asset and in the volatility index. In contrast, for the commodity market, this dependency occurs only after decomposing the jump sizes that affect the asset into positive and negative components.