A closed-form characterization of correlation in real options with Lévy processes

Abstract

This paper investigates the dynamic correlation between project value and investment cost in a real options framework with exponential Lévy processes. We derive a closed-form expression for correlation that captures both Brownian and jump-induced dependencies. Numerical simulations reveal time-varying, nonlinear behavior, the emergence of jump-induced outliers, and sublinear scaling between value and cost. These features significantly affect investment timing and valuation under uncertainty. Our findings highlight the importance of modeling structural shocks for optimal investment timing.