  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 time between observation dates.
Corrections due to this effect are calculated and compared with Monte-Carlo
results. Good agreement between analytical formula and numerical calculations
of VA values is demonstrated.
