Worst-Case Value-at-Risk of Non-Linear Portfolios
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 further 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. These models lead to new Worst-Case Polyhedral VaR (WCPVaR) and Worst-Case Quadratic VaR (WCQVaR) approximations, respectively. WCPVaR is a suitable VaR approximation for portfolios containing long positions in European options expiring at the end of the investment horizon, whereas WCQVaR is suitable for portfolios containing long and/or short positions in European and/or exotic options expiring beyond the investment horizon. We prove that WCPVaR and WCQVaR optimization can be formulated as tractable second-order cone and semidefinite programs, respectively, and reveal interesting connections to robust portfolio optimization. Numerical experiments demonstrate the benefits of incorporating non-linear relationships between the asset returns into a worst-case VaR model.
When requesting a correction, please mention this item's handle: RePEc:com:wpaper:017. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Anil Khuman)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.