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A risk-neutral equilibrium leading to uncertain volatility pricing

Johannes Muhle-Karbe () and Marcel Nutz ()
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Johannes Muhle-Karbe: Carnegie Mellon University
Marcel Nutz: Columbia University

Finance and Stochastics, 2018, vol. 22, issue 2, 281-295

Abstract: 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.

Keywords: Heterogeneous beliefs; Equilibrium; Derivative price bubble; Uncertain volatility model; Nonlinear expectation; 91B51; 91G20; 93E20 (search for similar items in EconPapers)
JEL-codes: D52 G12 G13 D53 (search for similar items in EconPapers)
Date: 2018
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