A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing
15 Pages Posted: 31 Dec 2016
Date Written: December 29, 2016
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
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