Decision Making in Incomplete Markets with Ambiguity -- A Case Study of a Gas Field Acquisition

Tinbergen Institute Discussion Paper 14-149/VI

52 Pages Posted: 2 Dec 2014

See all articles by Lin Zhao

Lin Zhao

University of Amsterdam

Sweder van Wijnbergen

Universiteit van Amsterdam; Tinbergen Institute; Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER)

Date Written: December 1, 2014


We apply utility indifference pricing to solve a contingent claim problem, valuing a connected pair of gas fields where the underlying process is not standard Geometric Brownian motion and the assumption of complete markets is not fulfilled. First, empirical data are often characterized by time-varying volatility and fat tails; therefore we use Gaussian GAS (Generalized AutoRegressive Score) and GARCH models, extending them to Student's t-GARCH and t-GAS. Second, an important risk (reservoir size) is not hedgeable. Thus markets are incomplete which also makes preference free pricing impossible and thus standard option pricing inapplicable. Therefore we parametrize the investor's risk preference and use utility indifference pricing techniques. We use Lease Square Monte Carlo simulations as a dimension reduction technique.

Moreover, an investor often only has an approximate idea of the true probabilistic model underlying variables, making model ambiguity a relevant problem. We show empirically how model ambiguity affects project values, and importantly, how option values change as model ambiguity gets resolved in later phases of the projects considered.

We show that traditional valuation approaches will consistently underestimate the value of project flexibility and in general lead to overly conservative investment decisions in the presence of time dependent stochastic structures.

Keywords: real options, time varying volatility and fat tails, GAS models, model ambiguity, decision making in incomplete markets, utility indifference pricing

JEL Classification: C61, D81, G01, G31, G34, Q40

Suggested Citation

Zhao, Lin and van Wijnbergen, Sweder, Decision Making in Incomplete Markets with Ambiguity -- A Case Study of a Gas Field Acquisition (December 1, 2014). Tinbergen Institute Discussion Paper 14-149/VI, Available at SSRN: or

Lin Zhao (Contact Author)

University of Amsterdam ( email )

Spui 21
Amsterdam, 1018 WB

Sweder Van Wijnbergen

Universiteit van Amsterdam ( email )

Roetersstraat 11
Amsterdam, 1018 WB
+31 20 525 4011 / 4203 (Phone)
+31-35-624 91 82 (Fax)

Tinbergen Institute

Burg. Oudlaan 50
Rotterdam, 3062 PA

Centre for Economic Policy Research (CEPR)

United Kingdom

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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