Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk

Christian-Oliver Ewald and Zhaojun Yang

Mathematical Methods of Operations Research, 2008, vol. 68, issue 1, 97-123

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 (Adv Futures Options Res 4:1–21, 1990) for the case of a complete market, in which the risk can be perfectly hedged with an appropriate spanning asset, by McDonald and Siegel (Q J Econ, 101:707–727, 1986), who include the incomplete case but assume that the agent is risk neutral toward idiosyncratic risk, and later by Henderson (Valuing the option to invest in an incomplete market, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=569865 , 2006) 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 (Investment under uncertainty, Princeton University Press, Princeton, 1994) as well as others, that the project value follows a geometric mean reverting 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. Copyright Springer-Verlag 2008

Keywords: Real options; Models of mean-reversion; Optimal control; Incomplete market models; C61; G11; G12; G31; E2 (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-007-0190-9 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:68:y:2008:i:1:p:97-123

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-007-0190-9

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().