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

25 Pages Posted: 10 Jan 2012 Last revised: 22 Oct 2012

See all articles by Ulrich Horst

Ulrich Horst

Humboldt University of Berlin

Michael Kupper

Humboldt University of Berlin - Department of Mathematics

Andrea Macrina

University College London; University of Cape Town (UCT)

Christoph Mainberger

Humboldt Universitaet zu Berlin, Department of Mathematics

Date Written: October 19, 2012

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.

Keywords: Continuous-time equilibrium, exponential utility, CAPM, affine processes, information-based asset pricing, implied volatility

JEL Classification: C62, D52, D53

Suggested Citation

Horst, Ulrich and Kupper, Michael and Macrina, Andrea and Mainberger, Christoph, Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models (October 19, 2012). Available at SSRN: https://ssrn.com/abstract=1982163 or http://dx.doi.org/10.2139/ssrn.1982163

Ulrich Horst

Humboldt University of Berlin ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

Michael Kupper

Humboldt University of Berlin - Department of Mathematics ( email )

Unter den Linden
Berlin, D-10099
Germany

Andrea Macrina

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

Christoph Mainberger (Contact Author)

Humboldt Universitaet zu Berlin, Department of Mathematics ( email )

Under den Linden 6
Berlin, 10099
Germany

HOME PAGE: http://www.math.hu-berlin.de/~mainberg

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