VAR for Nonlinear Instruments - Linear Approximation or Full Monte Carlo?

We investigate different methods for computing value-at-risk for nonlinear portfolios by applying them to portfolio compositions containing various option structures. Surprisingly, even for optioned portfolios, the results from relatively crude approximations such as the delta-normal method do not differ greatly from full Monte Carlo simulation approaches in many cases. Sometimes, however, the differences can become unacceptably large, particularly for short-maturity option positions, for highly nonlinear instruments such as straddles and strangles, and for long VaR horizons and high confidence levels. To identify portfolios where caution is warranted with simple linear approximations, we propose a measure to quantify the degree of nonlinearity in a portfolio. Using several example portfolios, we relate this measure to actual VaR errors caused by the use of approximation methods and find it to be a good indicator of VaR errors