Model-free hedge ratios and scale-invariant models

By Carol Alexander, Leonardo M. Nogueira. 2007

63 citations recorded by the source corpus.

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.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/2bebc675f3d5f9f4966651536cf4b17b0ef1b88c

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In Finance

1. H. Buhler
2. Ben Wood
3. Matthias R. Fengler
4. Josef Teichmann
5. Lukas Gonon

Citations in the corpus

• Arbitrage-free smoothing of the implied volatility surface (2009, methodology): “For a discussion of the financial implications of an option pricing function that is homogeneous in spot and strikes we refer to Renault (1997), Alexander and Nogueira (2007) and Fengler et al. (2007).”
• Deep hedging (2018, background): “Bates (2005), Alexander and Nogueira (2007), Sepp (2012) and Hull and White (2017).”