Critical Illness Insurance Pricing Using A Modified Option Approach Under Gamma Process

Abstract

Critical illness insurance protects against complex risks and high medical costs. This study proposes a premium model using a modified call option framework, where benefits are paid if medical expenses exceed a predefined claim limit. We examine two cases based on Indonesia’s National Health Insurance regulations: with and without an inpatient care class upgrade. The model employs the Gamma process to represent treatment costs and claim limits while analyzing the impact of parameters on insurance premiums. Results show that premiums increase with the cost-to-claim limit ratio in the non-upgraded model. In contrast, in the upgraded model, premiums rise as the claim limit increases, assuming expected costs exceed the limit.