An adaptive procedure for estimating coherent risk measures based on generalized scenarios

ABSTRACT Simulating coherent risk measures is potentially very computationally expensive. We present a procedure for generating a fixed-width confidence interval for a coherent risk measure based on a finite number of generalized scenarios. Computational experiments show that this procedure is much more efficient than standard methods, making simulation of coherent risk measures based on even a large number of generalized scenarios affordable. The procedure improves upon previous specialized methods by being reliably efficient when applied to simulation of generalized scenarios and portfolios with heterogeneous characteristics. We also show how robust the procedure’s performance is to violations of the normality assumption under which its statistical validity is proved, and study the magnitude of estimation error.