  Value-at-risk (VaR) has been playing the role of a standard risk measure
since its introduction. In practice, the delta-normal approach is usually
adopted to approximate the VaR of portfolios with option positions. Its
effectiveness, however, substantially diminishes when the portfolios concerned
involve a high dimension of derivative positions with nonlinear payoffs; lack
of closed form pricing solution for these potentially highly correlated,
American-style derivatives further complicates the problem. This paper proposes
a generic simulation-based algorithm for VaR estimation that can be easily
applied to any existing procedures. Our proposal leverages cross-sectional
information and applies variable selection techniques to simplify the existing
simulation framework. Asymptotic properties of the new approach demonstrate
faster convergence due to the additional model selection component introduced.
We have also performed sets of numerical results that verify the effectiveness
of our approach in comparison with some existing strategies.
