Jump-Diffusion model with currency uncertainty: A real option approach

Resum

This paper analyzes the investment decision under currency uncertainty using a real options framework where the project value follow a jump-diffusion process, while the investment cost a geometric Brownian motion (GBM). We derive the Hamilton-Jacobi-Bellman (HJB) equation and optimal investment threshold explicitly. The model is compared with a purely GBM-based approach to highlight the effect of jump risk. The results show that higher currency ratio and jump intensity greatly impact the investment threshold, encouraging earlier investment. Sensitivity analyses are conducted on key parameters highlighting their impact. Our findings provide insights into investment timing for industries and firms operating in volatile international markets, where
currency fluctuations are ever present.