Geometric Ergodicity of the MUCOGARCH(1,1) process

Robert Stelzer, Johanna Vestweber

Published 2017-01-26Version 1

For the multivariate COGARCH(1,1) volatility process we show sufficient conditions for the existence of a unique stationary distribution, for the geometric ergodicity and for the finiteness of moments of the stationary distribution. One of the conditions demands a sufficiently fast exponential decay of the MUCOGARCH(1,1) volatility process. Furthermore, we show easily applicable sufficient conditions for the needed irreducibility of the volatility process living in the cone of positive semidefinite matrices, if the driving L\'evy process is a compound Poisson process.