This paperpresents a novel framework for valuation and hedging of the insurer's net liability on a Guaranteed Minimum Maturity Benefit (GMMB) embedded in variable annuity (VA) contracts whose underlying mutual fund dynamics evolve under the influence of the regime-switching model. Numerical solutions for valuations and Greeks (i.e. valuation sensitivities with respect to model parameters) of GMMB under stochastic mortality are derived. Valuation 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 American male population. Sensitivity analysis is performed with respect to various parameters. The hedge effectiveness is assessed by comparing profit-and-loss performances for an unhedged and three statically hedged portfolios . The results provide a comprehensive analysis on valuation and hedging the longevity risk, interest rate risk and equity risk for the GMMB embedded in VAs, and highlight the benefits to insurance providers who offer those products .
In this paper, we adopted a net liability model which assesses both market risk on the liability side and revenue risk on the asset side for a Guaranteed Minimum Maturity Benefit (GMMB) embedded in variable annuity (VA) contracts . Numeric solutions for net liabilities, fair rate of fees and Greeks of GMMB are obtained by a more accurate and fast Fourier Space time-stepping (FST) algorithm. Monte Carlo results are provided for comparative purpose. The unhedged and three statically hedged portfolios are introduced, and their performances are assessed by comparing the short term and long term portfolio's volatility. Recently, we noticed FST algorithm can only be used to hedge the gross liability of GMMB and it leads to an incorrect result when applying FST algorithm to the net liability model. We have modified the method we used in the hedging part and obtained the reliable result now. They will be reported in near future .
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This paperpresents a novel framework for valuation and hedging of the insurer's net liability on
In this paper, we adopted a net liability model which assesses both market risk on the liability side and revenue risk on the asset side for
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whose underlying mutual fund dynamics evolve under the influence of the regime-switching model. Numerical solutions for valuations and Greeks (i.e. valuation sensitivities with respect to model parameters) of GMMB under stochastic mortality are derived. Valuation and hedging is performed using an accurate , fast and efficient Fourier Space Time-stepping
. Numeric solutions for net liabilities, fair rate of fees and Greeks of GMMB are obtained by a more accurate and fast Fourier Space time-stepping
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The mortality component of the model is calibrated to the American male population. Sensitivity analysis is performed with respect to various parameters. The hedge effectiveness is assessed by comparing profit-and-loss performances for an
Monte Carlo results are provided for comparative purpose. The
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. The results provide a comprehensive analysis on valuation and hedging the longevity risk, interest rate risk and equity risk for the GMMB embedded in VAs, and highlight the benefits to insurance providers who offer those products
are introduced, and their performances are assessed by comparing the short term and long term portfolio's volatility. Recently, we noticed FST algorithm can only be used to hedge the gross liability of GMMB and it leads to an incorrect result when applying FST algorithm to the net liability model. We have modified the method we used in the hedging part and obtained the reliable result now. They will be reported in near future