196185
20190316235832.0
doi
10.1287/mnsc.1120.1615
1526-5501
ARTICLE
Worst-Case Value at Risk of Nonlinear Portfolios
2013
2013
Journal Articles
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 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.
Value at risk
Derivatives
Robust optimization
Second-order cone programming
Semidefinite programming
Zymler, Steve
247589
Kuhn, Daniel
239987
Rustem, Berç
59
1
172-188
Management Science
http://pubsonline.informs.org/doi/abs/10.1287/mnsc.1120.1615
URL
252496
RAO
U12788
oai:infoscience.tind.io:196185
CDM
article
GLOBAL_SET
112541
EPFL-ARTICLE-196185
OTHER
NON-REVIEWED
PUBLISHED
ARTICLE