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A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing

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  • Johannes Muhle-Karbe
  • Marcel Nutz

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.

Suggested Citation

  • Johannes Muhle-Karbe & Marcel Nutz, 2016. "A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing," Papers 1612.09152, arXiv.org, revised Jan 2018.
    • Handle: RePEc:arx:papers:1612.09152
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    References listed on IDEAS

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    Cited by:

    1. Benedikt Geuchen & Katharina Oberpriller & Thorsten Schmidt, 2022. "Classical and deep pricing for Path-dependent options in non-linear generalized affine models," Papers 2207.13350, arXiv.org.
    2. Johannes Muhle-Karbe & Marcel Nutz & Xiaowei Tan, 2019. "Asset Pricing with Heterogeneous Beliefs and Illiquidity," Papers 1905.05730, arXiv.org, revised Mar 2020.
    3. Marcel Nutz & Jos'e A. Scheinkman, 2017. "Shorting in Speculative Markets," Papers 1705.05882, arXiv.org, revised Jul 2019.
    4. Marcel Nutz & José A. Scheinkman, 2020. "Shorting in Speculative Markets," Journal of Finance, American Finance Association, vol. 75(2), pages 995-1036, April.
    5. Marcel Nutz & José A. Scheinkman, 2017. "Supply and Shorting in Speculative Markets," NBER Working Papers 23751, National Bureau of Economic Research, Inc.
    6. Changhong Guo & Shaomei Fang & Yong He, 2023. "A Generalized Stochastic Process: Fractional G-Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-34, March.

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