S. Zymler, D. Kuhn, and B. Rustem: Worst-Case Value-at-Risk of Non-linear Portfolios

June 21, 2009

Portfolio optimization problems involving Value-at-Risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR over all return distributions of the derivative underliers with given first- and second-order moments.The derivative returns are modelled as convex piecewise linear or—by using a delta-gamma approximation—as (possibly non-convex) quadratic functions of the returns of the derivative underliers.