Computational Challenges for Value-at-Risk and Expected Shortfall : Chebyshev Interpolation to the Rescue?

Computational challenges associated with calculating risk measures are inherent to many applications in financial institutions. An example is the need to revalue portfolios of trading positions hundreds or thousands of times to determine the future distribution of their present values and risk measures such as Value-at-Risk and Expected Shortfall. This paper reports on an exploratory study in which recently popularised "smart grids" based on Chebyshev interpolation are compared to standard (uniform) grids as well as Taylor expansion when applied to this task. While generally outperforming other methods and despite their advantageous properties, Chebyshev grids are still subject to drawbacks such as difficult error control and the curse of dimensionality. They cannot yet be seen as a quantum leap in the calculation of risk measures. Ongoing research focussing on sparse grids and their approximation quality, however, is promising