Robust Risk Management of Portfolio of Derivatives

The last two decades have seen a proliferation of derivatives to meet the growing sophistication of participants in the nancial markets. Oddly enough, despite this proliferation of new assets, the efforts and progress to understand the overall impact of using such derivatives in one's portfolio have been rather slow. As a result, derivatives users are left with outdated tools that were designed for the more traditional assets, such as stocks or bonds, and are less useful, or even harmful, when it comes to these new assets. Derivatives need to be treated differently from the traditional assets for two reasons. First, their characteristics, i.e. the properties that describe their return distribution, can be signicantly different and therefore higher-order moments, especially skewness, become important. Secondly, the uncertainty arising from the estimation of these characteristics of the underlying assets of a derivative will be magnied in the value of the derivative. While it is generally accepted that computational or mathematical tools that investors increasingly use to aid their investment decision makings improve their control over uncertainty, this rather fundamental incompleteness in the existing tools is not desirable. This problem becomes especially acute for those investors with a conservative investment policy who can not afford to be exposed to such unquantifiable risk. These investors should pursue a portfolio that survives. Their portfolio must survive various market shocks that throughout the history without exceptions took away so much wealth from investors. This thesis therefore tries to address the following two questions. How do we optimally construct a portfolio when derivatives are considered? What do we do to minimise the model uncertainty inherent in derivatives? Looking ahead, we believe our work will have applications not only in the asset allocation, but also in pricing and hedging of derivatives.