Model-free hedge ratios and scale-invariant models

Alexander, Carol and Nogueira, Leonardo M (2007) Model-free hedge ratios and scale-invariant models. Journal of Banking & Finance, 31 (6). pp. 1839-1861. ISSN 0378-4266

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Abstract

A price process is scale-invariant if and only if the returns distribution is independent of the price measurement scale. We show that most stochastic processes used for pricing options on financial assets have this property and that many models not previously recognised as scale-invariant are indeed so. We also prove that price hedge ratios for a wide class of contingent claims under a wide class of pricing models are model-free. In particular, previous results on model-free price hedge ratios of vanilla options based on scale-invariant models are extended to any contingent claim with homogeneous pay-off, including complex, path-dependent options. However, model-free hedge ratios only have the minimum variance property in scale-invariant stochastic volatility models when price–volatility correlation is zero. In other stochastic volatility models and in scale-invariant local volatility models, model-free hedge ratios are not minimum variance ratios and our empirical results demonstrate that they are less efficient than minimum variance hedge ratios.

Item Type: Article
Keywords: Scale invariance; Model-free; Hedging; Minimum variance; Stochastic volatility; Local volatility
Schools and Departments: School of Business, Management and Economics > Business and Management
Subjects: H Social Sciences > HG Finance
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Depositing User: Carol Alexander
Date Deposited: 11 Sep 2012 14:15
Last Modified: 11 Sep 2012 14:15
URI: http://sro.sussex.ac.uk/id/eprint/40619
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