000196185 001__ 196185
000196185 005__ 20190316235832.0
000196185 0247_ $$2doi$$a10.1287/mnsc.1120.1615
000196185 022__ $$a1526-5501
000196185 037__ $$aARTICLE
000196185 245__ $$aWorst-Case Value at Risk of Nonlinear Portfolios
000196185 260__ $$c2013
000196185 269__ $$a2013
000196185 336__ $$aJournal Articles
000196185 520__ $$aPortfolio optimization problems involving value at risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR over all return distributions of the derivative underliers with given first- and second-order moments. The derivative returns are modelled as convex piecewise linear or—by using a delta–gamma approximation—as (possibly nonconvex) quadratic functions of the returns of the derivative underliers. These models lead to new worst-case polyhedral VaR (WPVaR) and worst-case quadratic VaR (WQVaR) approximations, respectively. WPVaR serves as a VaR approximation for portfolios containing long positions in European options expiring at the end of the investment horizon, whereas WQVaR is suitable for portfolios containing long and/or short positions in European and/or exotic options expiring beyond the investment horizon. We prove that—unlike VaR that may discourage diversification—WPVaR and WQVaR are in fact coherent risk measures. We also reveal connections to robust portfolio optimization.
000196185 6531_ $$aValue at risk
000196185 6531_ $$aDerivatives
000196185 6531_ $$aRobust optimization
000196185 6531_ $$aSecond-order cone programming
000196185 6531_ $$aSemidefinite programming
000196185 700__ $$aZymler, Steve
000196185 700__ $$0247589$$g239987$$aKuhn, Daniel
000196185 700__ $$aRustem, Berç
000196185 773__ $$j59$$tManagement Science$$k1$$q172-188
000196185 8564_ $$uhttp://pubsonline.informs.org/doi/abs/10.1287/mnsc.1120.1615$$zURL
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000196185 917Z8 $$x112541
000196185 937__ $$aEPFL-ARTICLE-196185
000196185 973__ $$rNON-REVIEWED$$sPUBLISHED$$aOTHER
000196185 980__ $$aARTICLE