An Enhanced Static Hedge: Using Two Symmetric Pairs of Options

<xref>Wu and Zhu (W-Z 2017)</xref> proposed a model-free approach for statically hedging options using an option portfolio. Recently, <xref>Guo and Liu (G-L 2023)</xref> extended W-Z’s scheme, mainly by replacing the naive Dupire equation in W-Z with a more general equation and introducing a better error measure. We advance W-Z’s scheme and G-L’s extension by developing a hedging portfolio consisting of <italic>two symmetric pairs</italic> of options (<italic>T-P hedge</italic>) to more precisely replicate the target option’s characteristics. This new T-P scheme enhances the prior schemes in two critical aspects: (1) It captures higher-order risk sensitivities of the target option, which are conclusively demonstrated to be indispensable for reducing hedging errors; (2) T-P hedge bypasses two issues, apart from several technical concerns, in the prior hedges: the need for a third strike, and the maturity restriction in hedging portfolio, thereby enhancing practical applicability. Comprehensive simulations within two classical models, particularly the empirical examinations using SPX options, strongly demonstrate that our strategy significantly enhances the hedging performance in accuracy and operational simplicity.