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Finance and Stochastics

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07.03.2018

A risk-neutral equilibrium leading to uncertain volatility pricing

verfasst von: Johannes Muhle-Karbe, Marcel Nutz

Erschienen in: Finance and Stochastics | Ausgabe 2/2018

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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.

Vorheriger Artikel The microstructural foundations of leverage effect and rough volatility

Nächster Artikel An expansion in the model space in the context of utility maximization

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As mentioned in the introduction, the fact that we do not explicitly model trading in the underlying is equivalent to the assumption that any tradable component of \(X\) is a martingale.

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Titel: A risk-neutral equilibrium leading to uncertain volatility pricing
verfasst von: Johannes Muhle-Karbe
Marcel Nutz
Publikationsdatum: 07.03.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Finance and Stochastics / Ausgabe 2/2018
Print ISSN: 0949-2984
Elektronische ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-018-0356-8

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