Anders Evenås och Ronny Alex

Hedging Strategy Optimization under Proportional Transaction Costs

Abstract

In this work hedging strategies for the European call option, the
Power call option and the Binary option, in a discrete time model and
under proportional transaction costs, are investigated. In
continuous time without transaction costs a replicating portfolio can
be created, but if transaction costs are introduced continuous
rebalancing will lead to ruin. In this work we assume that trading
only takes place at predefined time steps. We study delta and gamma to
formulate strategies and to decide when it is profitable to rebalance
the portfolio. Furthermore we use the European call option to hedge
the Power call option and the Binary option. The strategies will be
compared with an optimal buy and hold strategy. We will compare our
strategies by comparing worst case values, which are based on the
upper 5% quantile for the losses. All the results are numerically
simulated.

It turns out that the best results are obtained when the value of
gamma decides if the portfolio should be rebalanced or not. For the
Power call option and the Binary option it turns out that the strategy
can be much improved by hedging with European call options instead of
the underlying asset.