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Hedging large risks reduces the transaction costs

Farhat Selmi·Jean-Philippe Bouchaud
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Abstract

As soon as one accepts to abandon the zero-risk paradigm of Black-Scholes, very interesting issues concerning risk control arise because different definitions of the risk become unequivalent. Optimal hedges then depend on the quantity one wishes to minimize. We show that a definition of the risk more sensitive to the extreme events generically leads to a decrease both of the probability of extreme losses and of the sensitivity of the hedge on the price of the underlying (the `Gamma'). Therefore, the transaction costs and the impact of hedging on the price dynamics of the underlying are reduced.

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Farhat Selmi, Jean-Philippe Bouchaud. 2000-05-09. Hedging large risks reduces the transaction costs. https://arxiv.org/abs/cond-mat/0005148

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