When Firms Make Decisions: A New Constant Relative Risk Aversion Approach

We present a mathematical framework for valuing real options, considering agent risk preferences, where these choices are not necessarily risk-neutral, and we use a Constant Relative Risk Aversion utility function to capture this phenomenon. Our mathematical framework is based on a multiplicative binomial recombination tree, in which the transition probability, growth factors, and discount rate were modified. Our main conclusion shows that an option can be evaluated under the same conditions of risk neutrality as traditional frameworks, while considering the different risk preferences of the agent, verifying the traditional method that uses binomial trees corresponds to a particular case. We compare the numerical results against a modified Monte Carlo framework to test our method’s behavior. In the final section, the results of both techniques are presented for the most common real options. In addition to advancing the state of the art, this study provides algebraic formulations, broadens the scope of numerical frameworks, and captures empirical phenomena documented in the literature. These contributions offer a more comprehensive and realistic approach to real options valuation.