Statistical Hedging

Abstract

This note presents an extension of the Markoviz-type "mean-variance" portfolio optimisation approach over one period to portfolios of derivatives. Most notably, we show that once "writing off" parts of the portfolio is allowed, we naturally arrive at using "cash-invariant monotone hulls" a'la Filipovic/Kupper to construct sensible convex measures of risk.

We recommend using "Quadratic CVaR" as the most natural convex risk replacement for mean-variance optimisation. We also explain why classic Greek-based approaches are inferior to our approach for managing portfolios of derivatives.

This note summarises results presented at Global Derivatives 2013 and 2014 and provides a more generalised view on the problem at hand. This work contains little original contributions; its aim to motivate the use of convex risk measures and their construction via cash-invariant monotone hulls from a practitioner's point of view.

Keywords: Portfolio Optimization for Derivatives, Incomplete Market, Convex Risk Measure, Quadratic CVaR