Optimal Investment strategy with Currency Uncertainty

Currency uncertainty, characterized by fluctuations in exchange rates, significantly impacts  the valuation of investments and the timing of investment decisions. This paper develops a real  options framework incorporating a novel currency uncertainty ratio to capture the impact of  exchange rate fluctuations on investment timing. We analyze two cases: (i) project value follow ing a geometric Brownian motion (GBM) with a constant investment cost and (ii) both project  value and investment cost evolving as GBMs. Using stochastic control and optimal stopping  theory, we derive closed-form solutions for the investment thresholds and option values. We  further conduct a sensitivity analysis to explore how investment thresholds respond to changes  in currency risk, volatility, and discount rates. Our results suggest that currency uncertainty  significantly influences investment timing, often delaying investment decisions. These findings have important implications for multinational corporations, policymakers, and financial  analysts concerned with investment under foreign exchange risk.