On the Investment-Uncertainty Relationship in a Real Option Model with Stochastic Volatility

35 Pages Posted: 25 May 2011 Last revised: 16 Sep 2012

See all articles by Sai Hung Marten Ting

Sai Hung Marten Ting

The University of Sydney

Christian-Oliver Ewald

University of Glasgow; Høgskole i Innlandet

Wen-Kai Wang

National University of Kaohsiung - Department of Finance

Date Written: May 19, 2011

Abstract

We consider the classical investment timing problem in a framework where the instantaneous volatility of the project value is itself given by a stochastic process, hence lifting the old question about the investment-uncertainty relationship to a new level. Motivated by the classical cases of Geometric Brownian Motion (GBM) and Geometric Mean Reversion (GMR), we consider processes of similar functional form, but with Heston stochastic volatility replacing the constant volatility in the classical models. We refer to these processes as Heston-GBM and Heston-GMR.

For these cases we derive asymptotic solutions for the investment timing problem using the methodology introduced by Fouque et. al. (2000). In particular we show that compared to the classical cases with constant volatility, the question of whether additional stochastic volatility increases or decreases the investment threshold depends on the instantaneous correlation between the project value and the stochastic volatility. For the case of Heston-GBM we provide a closed form expression that measures this effect quantitatively, for the case of Heston-GMR we derive the sign of the effect analytically, using a type of maximum principle for ODEs. Various numerical examples are discussed and a comparative analysis is provided.

Keywords: Real options, investment-uncertainty relationship, stochastic volatility

JEL Classification: C6, E2

Suggested Citation

Ting, Sai Hung Marten and Ewald, Christian-Oliver and Wang, Wen-Kai, On the Investment-Uncertainty Relationship in a Real Option Model with Stochastic Volatility (May 19, 2011). Available at SSRN: https://ssrn.com/abstract=1846396 or http://dx.doi.org/10.2139/ssrn.1846396

Sai Hung Marten Ting

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

Christian-Oliver Ewald (Contact Author)

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Høgskole i Innlandet ( email )

Lillehammer, 2624
Norway

Wen-Kai Wang

National University of Kaohsiung - Department of Finance ( email )

700 Kaohsiung University Rd.
Nanzih District
Kaohsiung 803
Taiwan

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