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Mathematical Finance

Hedging with Uncertainty-Averse Preferences

Sebastian Herrmann: University of Michigan

Location:  Hill 705
Date & time: Tuesday, 28 February 2017 at 11:45AM - 11:45AM

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 penalize 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. If the reference model is a Black-Scholes model which is dynamically recalibrated to the market price of a liquidly traded vanilla option, delta-vega hedging is asymptotically optimal. The corresponding indifference price corrections are then determined by the disparity between the vegas, gammas, vannas, and volgas of the non-traded and the liquidly traded options.

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

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