Utility Based Pricing and Exercising of Real Options Under Geometric Mean Reversion and Risk Aversion Toward Idiosyncratic Risk

40 Pages Posted: 13 Jan 2007 Last revised: 14 Oct 2008

See all articles by Zhaojun Yang

Zhaojun Yang

Southern University of Science and Technology - Department of Finance

Christian-Oliver Ewald

University of Glasgow; Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance

Date Written: September 2007

Abstract

We study the classical real option problem in which an agent faces the decision if and when to invest optimally into a project. The investment is assumed to be irreversible. This problem has been studied by Myers and Majd [18] for the case of a complete market, in which the risk can be perfectly hedged with an appropriate spanning asset, by McDonald and Siegel [16], who include the incomplete case but assume that the agent is risk neutral toward idiosyncratic risk and later by Henderson [12] who studies the incomplete case with risk aversion toward idiosyncratic risk under the assumption that the project value follows a geometric Brownian motion. We take up Henderson's utility based approach but assume as suggested by Dixit and Pindyck [4] as well as others, that the project value follows a mean reverting geometric Ornstein-Uhlenbeck process. The mean reverting structure of the project value process makes our model richer and economically more meaningful. By using techniques from optimal control theory we derive analytic expressions for the value and the optimal exercise time of the option to invest.

Keywords: Real Options, Models of Mean-Reversion, Optimal Control, Incomplete Market Models

JEL Classification: C61, G11, G12, G31

Suggested Citation

Yang, Zhaojun and Ewald, Christian-Oliver, Utility Based Pricing and Exercising of Real Options Under Geometric Mean Reversion and Risk Aversion Toward Idiosyncratic Risk (September 2007). Available at SSRN: https://ssrn.com/abstract=956223 or http://dx.doi.org/10.2139/ssrn.956223

Zhaojun Yang

Southern University of Science and Technology - Department of Finance ( email )

No 1088, Xueyuan Rd.
District of Nanshan
Shenzhen, Guangdong 518055
China

HOME PAGE: http://fin.sustc.edu.cn/Case-detail-id-21.html

Christian-Oliver Ewald (Contact Author)

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance ( email )

Castlecliffe
The Scores
St. Andrews, Fife KY16 9AL
United Kingdom
+44(0)1334 462435 (Phone)

HOME PAGE: http://www.maths.usyd.edu.au/u/ewald/

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