Variable Annuities: Underlying Risks and Sensitivities

Chahboun, Imad; Hoover, Nathaniel

Working Paper

Variable Annuities: Underlying Risks and Sensitivities

Abstract: This paper presents a quantitative model designed to understand the sensitivity of variable annuity (VA) contracts to market and actuarial assumptions and how these sensitivities make them a potentially important source of risk to insurance companies during times of stress. VA contracts often include long dated guarantees of market performance that expose the insurer to multiple nondiversifiable risks. Our modeling framework employs a Monte Carlo simulation of asset returns and policyholder behavior to derive fair prices for variable annuities in a risk neutral framework and to estimate sensitivities of reserve requirements under a real?world probability measure. Simulated economic scenarios are applied to four hypothetical insurance company VA portfolios to assess the sensitivity of portfolio pricing and reserve levels to portfolio characteristics, modelling choices, and underlying economic assumptions. Additionally, a deterministic stress scenario, modeled on Japan beginning in the mid?90s, is used to estimate the potential impact of a severe, but plausible, economic environment on the four hypothetical portfolios. The main findings of this exercise are: (1) interactions between market risk modeling assumptions and policyholder behavior modeling assumptions can significantly impact the estimated costs of providing guarantees, (2) estimated VA prices and reserve requirements are sensitive to market price discontinuities and multiple shocks to asset prices, (3) VA prices are very sensitive to assumptions related to interest rates, asset returns, and policyholder behavior, and (4) a drawn?out period of low interest rates and asset underperformance, even if not accompanied by dramatic equity losses, is likely to result in significant losses in VA portfolios.

Keywords: insurance risk; market risk; variable annuities; derivative pricing; policyholder behavior;

JEL Classification: C15; G12; G17; G22; G23;