Decision-making in incomplete markets with ambiguity—a case study of a gas field acquisition

Abstract

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 generalized autoregressive score (GAS) and GARCH models, extending them to Student's t-GARCH and t-GAS. Second, an important risk (reservoir size) is not hedgeable. As a result, markets are incomplete which makes preference free pricing impossible and thus standard option pricing methodology inapplicable. Therefore, we parametrize the investor's risk preference and use utility indifference pricing techniques. We use Least Squares Monte Carlo simulations as a dimension reduction technique in solving the resulting stochastic dynamic programming problems. 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. 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.