Robust Hedging of Variance Swaps: Discrete Sampling & Co-maturing European Options

Abstract

In the practice of quantitative finance, model risk has raised significant concern and thus model-independent hedging is of particular interest to both academia and industry. In this thesis, we review two methods of constructing robust and model-independent hedging portfolios of variance swaps. One of them assumes a continuum of European options trade but does not require the underlying asset's price path to be continuous. However, the other assumes finite number of options quoted but requires the continuity of underlying asset's price path. We explore numerically the hedging performance as well as upper and lower bounds of several numerical examples by implementing these two methods. Finally, we try to combine these two methods and use an example to show an idea of a possible approach of doing this.