A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing

TL;DR

This paper develops a model of derivative pricing in a risk-neutral equilibrium with heterogeneous beliefs, revealing how speculative bubbles can form and how prices reflect model uncertainty.

Contribution

It introduces a unique equilibrium framework where derivative prices incorporate speculative value and bubbles, extending single-agent uncertainty models to multi-agent settings.

Findings

Existence of a unique equilibrium price under no short-selling constraint.

Equilibrium prices often include a bubble component exceeding autonomous valuations.

Mathematical form of the equilibrium price resembles single-agent models with model uncertainty.

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.