Hedging with Small Uncertainty Aversion

48 Pages Posted: 3 Jul 2015 Last revised: 17 Apr 2017

See all articles by Sebastian Herrmann

Sebastian Herrmann

University of Manchester

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

Frank Thomas Seifried

University of Trier

Date Written: May 20, 2016

Abstract

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their "distance" to a reference local volatility model. In the limit for small uncertainty aversion, this leads to explicit formulas for prices and hedging strategies in terms of the security’s cash gamma.

Keywords: volatility uncertainty, ambiguity aversion, option pricing and hedging, asymptotics

JEL Classification: G13, C61, C73

Suggested Citation

Herrmann, Sebastian and Muhle-Karbe, Johannes and Seifried, Frank Thomas, Hedging with Small Uncertainty Aversion (May 20, 2016). Finance and Stochastics, Vol. 21, No. 1, pp. 1-64, 2017, Swiss Finance Institute Research Paper No. 15-19, Available at SSRN: https://ssrn.com/abstract=2625965 or http://dx.doi.org/10.2139/ssrn.2625965

Sebastian Herrmann (Contact Author)

University of Manchester ( email )

Oxford Road
Manchester, N/A M13 9PL
United Kingdom

HOME PAGE: http://personalpages.manchester.ac.uk/staff/sebastian.herrmann

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

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