A risk-neutral equilibrium leading to uncertain volatility pricing

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 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 strong aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.

Affine processes under parameter uncertainty

“…The apparent risk of losses due to model mis-specification, called model risk fostered the development of strategies which are robust against model risk, typically leading to non-linear pricing rules. These robust strategies play a prominent role in the literature, see Denis and Martini (2006), Cont (2006), Eberlein et al (2014), Madan (2016), Acciaio et al (2016), Muhle-Karbe and Nutz (2018), Bielecki et al (2018) and the book Guyon and Henry-Labordère (2013), to name just a few references in this direction.…”

Asset pricing with heterogeneous beliefs and illiquidity

“…Uniform parabolicity is convenient to simplify the exposition, but of course results similar to ours could be obtained under different assumptions. When the support of X is not the whole space, the statements involving price functions and PDEs need to be restricted to a suitable domain (as, e.g., in Muhle‐Karbe & Nutz, 2018).…”

Asset Pricing with Heterogeneous Beliefs and Illiquidity

“…Uniform parabolicity is convenient to simplify the exposition, but of course results similar to ours could be obtained under different assumptions. When the support of X is not the whole space, the statements involving price functions and PDEs need to be restricted to a suitable domain (as, e.g., in [34]).…”