Speakers: Margaret Insley and Tony Wirjanto (University of Waterloo, Canada)
Title: Contrasting two approaches in real options valuation: contingent claims
versus dynamic programming

Abstract
This paper compares two well-known approaches for valuing a risky investment using real options theory: contingent claims (CC) with risk neutral valuation and dynamic programming (DP) using a risk adjusted discount rate. In theory, the correct risk adjusted discount rate will depend on the value and volatility of an investment and hence will not in general be constant. In practice, however, many researchers choose a constant risk adjusted discount rate for simplicity. A proof is presented which shows that, except under certain restrictive assumptions, DP using a constant discount rate and CC will not yield the same solutions for investment value. A few special cases are considered for which CC and DP with a constant discount rate are consistent with each other. An optimal timber harvesting example is presented to illustrate that the values obtained using the two approaches can differ significantly particularly when timber price is assumed to be mean reverting. Further, the implied risk adjusted discount rate calculated from CC is found to vary with the stochastic state variable and stand age. We conclude that for real options problems the CC approach should be used, since use of the correct stochastic discount rate results in unnecessarily complex pricing equations.