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arXiv · 1612.09152

A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing

Johannes Muhle-Karbe·Marcel Nutz
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Abstract

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.

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Johannes Muhle-Karbe, Marcel Nutz. 2018-01-03. A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing. https://arxiv.org/abs/1612.09152

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