# 14-149/VI (2014-12-01)

Lin Zhao, University of Amsterdam; Sweder van Wijnbergen, University of Amsterdam
real options, time varying volatility and fat tails, GAS models, model ambiguity, decision making in incomplete markets, utility indifference pricing
JEL codes:
C61, D81, G01, G31, G34, Q40

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.