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The theory of affine processes on the space of positive semidefinite d x dmatrices has been established in a joint work with Cuchiero, Filipovi\'c andTeichmann (2011). We confirm the conjecture stated therein that in dimension dgreater than 1 this process class does not exhibit jumps of infinite totalvariation. This constitutes a geometric phenomenon which is in contrast to thesituation on the positive real line (Kawazu and Watanabe, 1974). As anapplication we prove that the exponentially affine property of the Laplacetransform carries over to the Fourier-Laplace transform if the diffusioncoefficient is zero or invertible.

Affine processes on positive semidefinite d x d matrices have jumps of finite variation in dimension d > 1