Out-of-Model Adjustments of Variable Annuities

Abstract

This paper studies the model risk of the Black-Scholes (BS) model in pricing and risk-managing variable annuities motivated by its wide usage in the insurance industry. Specifically, we derive a model-free decomposition of the no-arbitrage price of the variable annuity into the BS model price in conjunction with three out-of-model adjustment terms. This sheds light on all risk drivers behind the product, that is, spot price, realized volatility, future smile, and sub-optimal withdrawal. We further investigate the efficacy of the BS-based hedging strategy given the market diverges from the model assumptions. We disclose that the spot price risk can always be eliminated by the strategy and the hedger's cumulative P\&L exhibits gradual slippage and instantaneous leakage. We finally show that the pricing, risk and hedging models can be separated from each other in managing the risks of variable annuities.

Tasks

Reproductions