Hedging Basket Options by Using a Subset of Underlying Assets

The purpose of this paper is to investigate the use of Principal Component Analysis in finding the efficient subset of underlying assets for hedging European basket options. This asset selection technique can be used together with other hedging strategies to enhance the hedging performance. Meanwhile, it become practical and essential when some of the underlying assets are illiquid or even not available to be traded. As an illustration, the optimal subset of assets is combined with a static hedging strategy that super-replicates a basket option with plain vanilla options on all the underlying assets with optimal strike prices. Through the combination of this super-hedging strategy and the newly-developed asset selection technique, we get a static hedging portfolio consisting of plain vanilla options only on the subset of dominant assets with optimal strikes. The strikes are chosen according to certain optimal criteria which depend on the risk attitude of investors while hedging basket options. The first hedging strategy could be a super-replication to eliminate all risks. Alternatively given a constraint on the investment into the hedge, optimal strikes are computed by minimizing a particular risk measure, e.g., variance of the hedging error or expected shortfall. Hence, the newly-developed static hedging portfolio by a subset of underlying assets is indeed to gain a tradeoff between the reduced hedging costs and the successful hedge. Through a numerical analysis, it is concluded that even without considering transaction costs hedging by using only a subset of assets works well particularly for inand at-the-money basket options: a small hedging error is achieved with a relatively low hedging cost.