We study the destabilising effect of dynamic hedging strategies on the price of the underlying asset in the presence of transaction costs. Once transaction costs are taken into account, continuous portfolio re-hedging is no longer an optimal strategy. Using a non-optimising (local in time) strategy for portfolio rebalancing, explicit dynamics for the price of the underlying asset are derived, focusing in particular on excess volatility and feedback effects of these portfolio insurance strategies. Moreover, it is shown how these latter depend on the heterogeneity of the insured payoffs. Finally, conditions are derived under which it may be still reasonable, from a practical viewpoint, to implement Black-Scholes strategies.
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