A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing

18 Pages Posted: 31 Dec 2016 Last revised: 5 Jan 2018

See all articles by Johannes Muhle-Karbe

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

Marcel Nutz

Columbia University

Date Written: January 3, 2018


We study the formation of derivative prices in equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that the derivative cannot be shorted, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with strong aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.

Keywords: Heterogeneous Beliefs, Equilibrium, Derivative Price Bubble, Uncertain Volatility Model, Nonlinear Expectation

Suggested Citation

Muhle-Karbe, Johannes and Nutz, Marcel, A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing (January 3, 2018). Available at SSRN: https://ssrn.com/abstract=2891478 or http://dx.doi.org/10.2139/ssrn.2891478

Johannes Muhle-Karbe (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
United Kingdom

HOME PAGE: http://www.ma.imperial.ac.uk/~jmuhleka/

Marcel Nutz

Columbia University ( email )

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