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A risk-neutral equilibrium leading to uncertain volatility pricing

Author

Listed:
  • Johannes Muhle-Karbe

    (Carnegie Mellon University)

  • Marcel Nutz

    (Columbia University)

Abstract

We study the formation of derivative prices in an equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, 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 worst-case aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.

Suggested Citation

  • Johannes Muhle-Karbe & Marcel Nutz, 2018. "A risk-neutral equilibrium leading to uncertain volatility pricing," Finance and Stochastics, Springer, vol. 22(2), pages 281-295, April.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-018-0356-8
    DOI: 10.1007/s00780-018-0356-8
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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 & José A. Scheinkman, 2020. "Shorting in Speculative Markets," Journal of Finance, American Finance Association, vol. 75(2), pages 995-1036, April.
    4. 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.
    5. Johannes Muhle‐Karbe & Marcel Nutz & Xiaowei Tan, 2020. "Asset pricing with heterogeneous beliefs and illiquidity," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1392-1421, October.

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    More about this item

    Keywords

    Heterogeneous beliefs; Equilibrium; Derivative price bubble; Uncertain volatility model; Nonlinear expectation;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

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