Ambiguous volatility and asset pricing in continuous time

TL;DR

This paper develops a continuous-time asset pricing model incorporating ambiguity about volatility and drift, leading to incomplete markets and interval-based pricing, with equilibrium analysis and a version of the C-CAPM.

Contribution

It introduces a utility-based model capturing ambiguity in volatility and drift, extending asset pricing theory to account for market incompleteness and equilibrium effects.

Findings

Ambiguous volatility causes market incompleteness and prevents perfect hedging.

Pricing is determined up to intervals due to ambiguity.

A version of the C-CAPM is derived showing effects of ambiguity on asset returns.

Abstract

This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging arguments. Ambiguous volatility implies market incompleteness that rules out perfect hedging. Consequently, hedging arguments determine prices only up to intervals. However, sharper predictions can be obtained by assuming preference maximization and equilibrium. Thus we apply the model of utility to a representative agent endowment economy to study equilibrium asset returns. A version of the C-CAPM is derived and the effects of ambiguous volatility are described.