Stochastic Discount Factors and Real Options

This paper uses the stochastic discount factor (SDF) to price real options and introduces the expected discounted shortfall (EDS) risk measure to control risk. A multivariate covariance based SDF modelling framework is described. Explicit formulae linking the correlation matrix to the risk premium are derived for assets prices following both Brownian and Ornstein-Uhlenbeck processes. Applying the SDF to real option problems simplifies calculations and economic assumptions by removing the requirement for replicating portfolios.The SDF method does not identify a hedging portfolio, so other risk control methods have to be used to compensate. EDS is a coherent, multi-period risk measure that calculates the present value of the risk to the shareholder, that cashflows are insufficient. An example real option is included, focusing on cashflow, using the SDF approach to measure the change in return and the EDS risk measure to price the increase in risk. The changing risk and return profile over time is also studied.