A Note on Hedging with Local and Stochastic Volatility Models

13 Pages Posted: 3 Nov 2008 Last revised: 22 Jun 2016

See all articles by Fabio Mercurio

Fabio Mercurio

Bloomberg L.P.

Massimo Morini

Algorand Foundation; Bocconi University

Date Written: November 3, 2008

Abstract

The behaviour of a smile model when applied to hedging should be consistent with market evidence that asset prices and market smiles move in the same direction (Hagan et al. 2002). Local volatility models are criticized because not consistent with this desired behaviour, and this has been an important driver towards the use of stochastic volatility models.

In this work we perform a simple analysis showing that, if we take into account explicitly the correlation between stochastic volatility and underlying asset which is typical of the most common stochastic volatility models, the hedging behaviour of stochastic volatility models does not always conform with the desired behaviour of a smile model in hedging.

With further simple tests we show that the behaviour of local volatility and stochastic volatility models calibrated to market skew is less different than assumed in current market wisdom. Both approaches, when used consistently with model assumptions, do not show the desired behaviour in hedging, while for both models the desired behaviour is obtained in market practice by hedging techniques which are not fully consistent with rigorous model assumptions.

Keywords: hedging, local volatility, stochastic volatility, sabr

JEL Classification: G13

Suggested Citation

Mercurio, Fabio and Morini, Massimo, A Note on Hedging with Local and Stochastic Volatility Models (November 3, 2008). Available at SSRN: https://ssrn.com/abstract=1294284 or http://dx.doi.org/10.2139/ssrn.1294284

Fabio Mercurio

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

Massimo Morini (Contact Author)

Algorand Foundation ( email )

1 George Street
049145
Singapore
20144 (Fax)

Bocconi University ( email )

Via Sarfatti, 25
Milan, MI 20136
Italy

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