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Pricing Two Heterogeneous Trees

Published online by Cambridge University Press:  01 June 2011

Nicole Branger ,
Christian Schlag  and
Lue Wu
Nicole Branger
Affiliation:
Finance Center Münster, Westfälische Wilhelms-Universität Münster, Universitätsstr. 14-16, 48143 Münster, Germany. [email protected]
Christian Schlag
Affiliation:
Goethe University, House of Finance, Grüneburgplatz 1, 60323 Frankfurt am Main, Germany. [email protected]
Lue Wu
Affiliation:
Goethe University, House of Finance, Grüneburgplatz 1, 60323 Frankfurt am Main, Germany. [email protected]
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Abstract

We consider a Lucas-type exchange economy with two heterogeneous stocks (trees) and a representative investor with constant relative risk aversion. The dividend process for one stock follows a geometric Brownian motion with constant and known parameters. The expected dividend growth rate for the other tree is stochastic and in general unobservable, although there may be a signal from which the investor can learn about its current value. We find that the equilibrium quantities in our model significantly depend on the information structure and on the level of risk aversion. While an observable stochastic drift mainly makes the economy more risky, a latent expected growth rate process with learning significantly changes the equilibrium price-dividend ratios, price reactions to dividend and drift innovations, expected returns, volatilities, correlations, and differences between the stocks. These effects are the more pronounced the more risk averse the representative investor.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 46 , Issue 5 , October 2011 , pp. 1437 - 1462
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2011

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