Imperial College London
Alternate

Emeritus ProfessorBercRustem

Faculty of Engineering, Department of Computing

Emeritus Professor
 
 
 
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Contact

 

+44 (0)20 7594 8345b.rustem Website

 
 
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Assistant

 

Dr Amani El-Kholy +44 (0)20 7594 8220

 
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Location

 

361Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Zymler:2012:10.1287/mnsc.1120.1615,
author = {Zymler, S and Kuhn, D and Rustem, B},
doi = {10.1287/mnsc.1120.1615},
journal = {Management Science},
title = {Worst-Case Value-at-Risk of Non-Linear Portfolios},
url = {http://dx.doi.org/10.1287/mnsc.1120.1615},
year = {2012}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Zymler,S
AU  - Kuhn,D
AU  - Rustem,B
DO  - 10.1287/mnsc.1120.1615
PY  - 2012///
SN  - 0025-1909
TI  - Worst-Case Value-at-Risk of Non-Linear Portfolios
T2  - Management Science
UR  - http://dx.doi.org/10.1287/mnsc.1120.1615
ER  -
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