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

We apply the recently developed sampling algorithm, called random orthogonal matrix (ROM) simulation by Ledermann et al. [3], to compute VaR of a market risk portfolio. Typically, the covariance matrix has a large influence on ROM VaR. But VaR, being a lower quantile of the portfolio return distribution, is also much impacted by the skewness and kurtosis of the risk factor returns. With ROM VaR it is possible to stress test risk factors under adverse market conditions by targeting other sample moments that are consistent with periods of financial crisis. In particular, the important effects of skewness or kurtosis in the tail of the portfolio returns can be incorporated in ROM VaR. In a simulation study, we integrate ROM VaR into other methods that take into account skewness and kurtosis, namely the Cornish-Fisher VaR approximation and a robust approximation to the Chebyshev-Markov VaR upper bound in Hürlimann [7].