Pricing Variable Annuity Contracts with High-Water Mark Feature

Variable annuities (VA) are popular insurance products. VAs provides the insured with a guaranteed accumulation rate on their premium at maturity. In addition, the insured may receive extra benefit if returns of underlying funds are high enough. Here we consider a special case of VA with high-water mark feature and Guaranteed Minimum payment reset. In Black-Scholes model for underlying fund we derive explicit pricing formula for this type of contract. The value of VA contracts depends on the tim...