Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models

TL;DR

This paper develops a continuous-time equilibrium model for capital asset pricing with multiple agents and securities, incorporating affine processes and information-based pricing to analyze asset dynamics and option implied volatility.

Contribution

It introduces a semi-explicit pricing framework for equilibrium asset prices in models with incomplete markets and exponential utility agents, linking risk aversion to implied volatility.

Findings

Equilibrium exists when agents have exponential utility and endowments are spanned by securities.

Optimal trading strategies are constant in equilibrium.

Risk aversion significantly influences the implied volatility surface.

Abstract

We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have exponential utility functions and the individual endowments are spanned by the securities, an equilibrium exists and the agents' optimal trading strategies are constant. Affine processes, and the theory of information-based asset pricing are used to model the endogenous asset price dynamics and the terminal payoff. The derived semi-explicit pricing formulae are applied to numerically analyze the impact of the agents' risk aversion on the implied volatility of simultaneously-traded European-style options.