Pricing Variable Annuity Contracts with High-Water Mark Feature

TL;DR

This paper derives explicit pricing formulas for variable annuity contracts with high-water mark features under the Black-Scholes model, incorporating observation timing effects and validating results with Monte Carlo simulations.

Contribution

It introduces a novel explicit pricing formula for high-water mark variable annuities considering observation timing effects, validated through numerical methods.

Findings

Analytical formulas closely match Monte Carlo simulations.

Observation timing significantly impacts VA valuation.

Explicit pricing formulas improve computational efficiency.

Abstract

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.