The shadow cost includes two components. The first component is the product of pure information cost due to imperfect knowledge and heterogeneous expectations. The second component represents the additional cost caused by the short-selling constraint. Information costs are linked to Merton's (1987) model of capital market equilibrium with incomplete information, CAPMI. This model is extended by Wu, Li and Wei (1996) who propose an incomplete-information capital market equilibrium with heterogeneous expectations and short sale restrictions, GCAPM. This model is used in our paper to provide for the first time in the literature analytic solutions for derivatives in the presence of both shadow costs of incomplete information and short sales.
Shadow costs are used in standard discounted cash flow techniques and real options. The justification of shadow costs in real projects is based on the observation that R&D needs to be done before investment decisions. The main results regarding real options and shadow costs of incomplete information and short sales are proposed by extending the analysis in Bellalah (1999, 2000) and Bellalah and Wu (2009).
Our results have important implications in terms of pricing derivative assets and different types of real options. In particular, this framework can be easily implemented in investment decisions and the valuation of flexibility embedded in real projects. In fact, several investment decisions under uncertainty can be reformulated and their results can be implemented in the presence of incomplete information and investment constraints.