Development of the Black–Scholes Model for Determining Insurance Premiums to Mitigate the Risk of Disaster Losses Using the Principles of Mutual Cooperation and Regional Economic Growth

Abstract

The frequency and economic damage of natural disasters have increased globally over the last two decades due to climate change. This increase has an impact on the disaster insurance field, particularly in the calculation of premiums. Many regions have a shortcoming in employing insurance because the premium is too high compared with their budget allocation. As one of the solutions, the premium calculation can be developed by applying the cross-subsidies mechanism based on economic growth. Therefore, this research aims to develop premium models of natural disaster insurance that uniquely involve two new variables of an insured region: cross-subsidies and the economic growth rate. Another novelty is the development of the Black–Scholes model, considering the two new variables, and it is used to formulate the premium model. Following the modeling process, this study uses the model to estimate the premiums for natural disaster insurance in each province of Indonesia. The estimation results show that all new variables involved in the model novelties significantly affect the premiums. This research can be used by insurance companies to determine the premium of natural disaster insurance, which involves cross-subsidies and economic growth.