Out-of-Model Adjustments of Variable Annuities

TL;DR

This paper analyzes the limitations of the Black-Scholes model in pricing and hedging variable annuities, proposing a model-free decomposition and examining hedging effectiveness amidst market deviations.

Contribution

It introduces a model-free decomposition of variable annuity prices and evaluates the effectiveness of BS-based hedging strategies under market divergence.

Findings

Spot price risk can be eliminated by hedging

Hedging leads to gradual slippage and instantaneous leakage

Pricing, risk, and hedging models can be managed separately

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.