Further properties of random orthogonal matrix simulation

Targeting Kollo skewness with random orthogonal matrix simulation

“…In addition to the ability to match the exact mean and covariance matrix, ROM simulation is generally much faster than MC simulation, especially in high-dimensional systems, because samples are generated by simply changing R n to another random rotation matrix and performing the required matrix multiplications. See Ledermann and Alexander (2012) for the classification of different types of rotation matrix and their effects on ROM simulation sample characteristics.…”

“…It is based on the premise of exactly matching a target mean, covariance matrix and certain higher moments with every simulation. Several developments have extended the original paper, for instance, Ledermann and Alexander (2012) investigate the effect of different random rotation matrices on ROM simulation sample characteristics. And Hürlimann (2013) presents a very significant theoretical development of ROM simulation by extending the basic L matrices (which are fundamental to ROM simulation, as we shall see below) to a much broader class of generalised Helmert-Ledermann (GHL) matrices, thereby increasing flexibility and scope of ROM simulation.…”

Market Value-At-Risk: ROM Simulation, Cornish-Fisher Var and Chebyshev-Markov Var Bound

“…[2], Chap. 4), we concentrate here on the recent and important sampling algorithm called random orthogonal matrix (ROM) simulation, which is introduced in [3] (see also [4,5,6]). The authors describe this novel Monte Carlo algorithm as follows:…”