Pricing and hedging GLWB in the Heston and in the Black-Scholes with stochastic interest rate models

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• 作者：Ludovic Goudenè ; ge^a ; ^{ludovic.goudenege@math.cnrs.fr" class="auth_mail" title="E-mail the corresponding author} ; Andrea Molent^b ; ^{andrea.molent@phd.units.it" class="auth_mail" title="E-mail the corresponding author} ; Antonino Zanette^c ; ^{antonino.zanette@uniud.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Variable annuities ; GLWB pricing ; Stochastic volatility ; Stochastic interest rate ; Optimal withdrawal
• 刊名：Insurance: Mathematics and Economics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：70
• 期：Complete
• 页码：38-57
• 全文大小：2072 K

文摘

Valuing Guaranteed Lifelong Withdrawal Benefit (GLWB) has attracted significant attention from both the academic field and real world financial markets. As remarked by Forsyth and Vetzal (2014) the Black and Scholes framework seems to be inappropriate for such a long maturity products. They propose to use a regime switching model. Alternatively, we propose here to use a stochastic volatility model (Heston model) and a Black–Scholes model with stochastic interest rate (Hull–White model). For this purpose we present four numerical methods for pricing GLWB variables annuities: a hybrid tree-finite difference method and a Hybrid Monte Carlo method, an ADI finite difference scheme, and a Standard Monte Carlo method. These methods are used to determine the no-arbitrage fee for the most popular versions of the GLWB contract, and to calculate the Greeks used in hedging. Both constant withdrawal and optimal withdrawal (including lapsation) strategies are considered. Numerical results are presented which demonstrate the sensitivity of the no-arbitrage fee to economic, contractual and longevity assumptions.