Value at Risk (VAR) in Real Options Analysis

Abstract

Cash flow from operations can be controlled using real options. In this normative paper, we derive numerically in a univariate discrete time model, extension of (Kulatilaka, 1988), the expanded NPV of an industrial investment and, simultaneously, state variable thresholds for the whole life of the project to optimally exercise real options. In this framework, we model the whole distribution of expanded NPV using a Markov Chain Monte Carlo method, computing forward the same NPV previously derived in a backward induction process. A number of original results is derived for an all equity firm. Cash flow distribution and CfaR is derived for each epoch in the life of the project. A VaR for the expanded NPV at time zero is derived. The intuition of (Trigeorgis, 1996) page 123 about the risk controlling properties of real options is proved and quantified. These new methods have been applied to a numerical example in shipping finance.

Keywords: Real Options, Value at Risk, VaR, Cash Flow at Risk, CFaR, C-FaR, Monte Carlo, Markov Chain, Cost Volume Profit equation, mapping equation, Corporatemetrics, NERA, Risk Capital Management Partners, shipping finance, VLCC, Panamax, dry bulk carrier, time charter, GMM, MLE, OLS. Option to wait

JEL Classification: C15, C22, G13, G31