Jump Activity Analysis for Affine Jump-Diffusion Models: Evidences from the Commodity Market

The objective of this paper is to perform a joint analysis of jump activity for commodities and their respective volatility indices. Exploiting the property that for affine jump-diffusion models a volatility index, which is quoted on the market, is an affine function of the instantaneous volatility state variable (thus turning this quantity observable), 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 and the gold pair GLD/GVZ we find strong evidence that for these two markets the asset and its volatility have disjoint jumps. This result contrasts with existing results for the equity market and underpins a very specific nature of the commodity market. The results are further confirmed by analysing jump size distributions using a copula methodology.