Investment-Risk Protection Rider for Unit-Linked Insurance

Abstract

This paper designs an investment-risk protection rider that provides annual return bounds (a floor and a cap) at no explicit cost to the policyholder. The study models two scenarios using the Indonesia Stock Exchange Composite Index (IHSG) as the underlying asset: the first assumes the availability of derivative options to form a zero-cost collar, while the second assumes no options are available, forcing the company to use delta-neutral dynamic hedging. A primary novelty of this research is the demonstration of theoretical option pricing on non-normal return assets and the formulation of a "Semi Non-homogenous Double-Exponential Jump Diffusion" (SNDEJD) model, which is developed to resolve an analytical calculation issue found in the original Non-homogenous Double-Exponential Jump Diffusion (NDEJD) model's pricing formula, thereby allowing for theoretical option pricing while capturing long-term parameter shifts. The study concludes that if options are available, the rider is highly viable, offering a 0% return floor and a median cap of 14.9% with no risk to the insurer. However, the delta-neutral dynamic hedging approach is found to be ineffective and risky, as the Black-Scholes hedging model fails to cover the jump risks in the non-normal IHSG returns, leaving the company exposed to significant losses unless a much lower cap is set.