2022/08/26 by Zhiyi Shen, Shen, Zhiyi
Social Sciences · Economics, Econometrics and Finance · #Insurance, Mortality, Demography, Risk Management #Stochastic processes and financial applications #Insurance and Financial Risk Management
paper · pdf · doi:10.48550/arxiv.2208.12838
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.