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 Michigan at Ann Arbor

Johannes Muhle-Karbe

Carnegie Mellon University - Department of Mathematical Sciences

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 Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

HOME PAGE: http://www-personal.umich.edu/~sherrma/

Johannes Muhle-Karbe

Carnegie Mellon University - Department of Mathematical Sciences ( email )

Pittsburgh, PA 15213-3890
United States

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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