Pricing and hedging of guaranteed minimum benefits under regime-switching and stochastic mortality |
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| Institution: | 1. School of Mathematical Sciences, Peking University, Beijing 100871, PR China;2. Center for Statistical Science, Peking University, Beijing 100871, PR China;1. Department of Information and Financial Management and Institute of Finance, National Chiao-Tung University, Taiwan;2. Department of Finance, National Central University, Taiwan;3. Risk and Insurance Research Center, College of Commerce, National Chengchi University, Taiwan;1. Department of Mathematics and Statistics, York University, Toronto, Canada;2. Schulich School of Business, Finance Area, York University, Toronto, Canada;1. School of Risk Management, Insurance, and Actuarial Science, St. John’s University, United States;2. Insurance/Risk Management & Business Economics/Policy, University of Pennsylvania - The Wharton School, United States;1. Department of Mathematics, University of Illinois at Urbana-Champaign, United States of America;2. School of Finance, Nanjing University of Finance and Economics, PR China |
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| Abstract: | This paper presents a novel framework for pricing and hedging of the Guaranteed Minimum Benefits (GMBs) embedded in variable annuity (VA) contracts whose underlying mutual fund dynamics evolve under the influence of the regime-switching model. Semi-closed form solutions for prices and Greeks (i.e. sensitivities of prices with respect to model parameters) of various GMBs under stochastic mortality are derived. Pricing and hedging is performed using an accurate, fast and efficient Fourier Space Time-stepping (FST) algorithm. The mortality component of the model is calibrated to the Australian male population. Sensitivity analysis is performed with respect to various parameters including guarantee levels, time to maturity, interest rates and volatilities. The hedge effectiveness is assessed by comparing profit-and-loss distributions for an unhedged, statically and semi-statically hedged portfolios. The results provide a comprehensive analysis on pricing and hedging the longevity risk, interest rate risk and equity risk for the GMBs embedded in VAs, and highlight the benefits to insurance providers who offer those products. |
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| Keywords: | Variable annuity Guaranteed Minimum Benefits (GMB) Fourier Space Time-stepping (FST) algorithm Mortality risk Interest rate risk |
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