Pricing Modern Life Insurance Products using Phase-Type Models for Iran

Due to their flexible benefits, equity-linked products are becoming more and more common in the life insurance industry.The present study takes into account the guaranteed minimum death benefit and high-water benefit as two life insurance products. In addition, the underlying asset process is subjected to the jump-diffusion process with phase-type jumps. First, for modeling the lifetime data taken from the Iranian and UK life tables, we chose Canonical Form 1 rather than the Coxian form of phase-type distribution. The two most recent programs, mapfit.r and EMpht.jl , can evaluate this fit. Additionally, the Monte-Carlo approach is used to compare the variability in both products' prices for each country with varied interest and discount rates.The K-S test demonstrated an adequate fit to Iran's lifetime data with 150 phases and a 76.7-year life expectancy (Iran did not have gender-separated data), and UK lifetime data with 200 phases with an 81.8-year life expectancy. Additionally, using mapfit.r , running times for CF1 are less than 20 minutes as opposed to those for Coxian. The outcomes suggest that the prices differ in terms of interest rate, discount rate, the number of fitting phases, and the value of the underlying asset. Additionally, the lack of accuracy in modeling will result in overpricing. The prices ultimately are more volatile the larger the discount rate.