Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging

44 Pages Posted: 24 Nov 2015 Last revised: 18 Nov 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

Date Written: January 23, 2017

Abstract

We study option pricing and hedging with uncertainty about a Black-Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this vanilla option, delta-vega hedging is asymptotically optimal in the limit for small uncertainty aversion. The corresponding indifference price corrections are determined by the disparity between the vegas, gammas, vannas, and volgas of the non-traded and the liquidly traded options.

Keywords: model uncertainty, recalibration, delta-vega hedging, small uncertainty aversion, asymptotics

JEL Classification: G13, C61, C73

Suggested Citation

Herrmann, Sebastian and Muhle-Karbe, Johannes, Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging (January 23, 2017). Finance and Stochastics, Vol. 21, No. 4, pp. 873-930, 2017; Swiss Finance Institute Research Paper No. 15-52. Available at SSRN: https://ssrn.com/abstract=2694718 or http://dx.doi.org/10.2139/ssrn.2694718

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

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