Timing is (almost) everything: Real options, extreme value theory, climate adaptation, and flood risk management.

Flood risk has become a major concern in many regions due to socio-economic growth and rising water levels. In this paper, we introduce a real options model that integrates the Generalized Additive Models for Location, Scale, and Shape framework with Extreme Value Theory to evaluate adaptation measures for flood risk management. Our model allows for uncertain water level rise, climate indices and growing loss exposure. In a case study of flood risk management for New York City, we find that while immediate investment in a barrier and dike project can provide a substantial net present value ($10.96 billion), investing at the optimal time can significantly improve the investment value by 54.84%. Our sensitivity analysis suggests that discount rate is the most important parameter, followed by the mean level of water rise and the water level rise uncertainty. We also find that investment delay is longer when the discount rate or the water level rise uncertainty is higher or when the expected water level rise is lower.