Pricing annuity guarantees under a double regime-switching model |
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| Institution: | 1. School of Finance and Statistics, East China Normal University, Shanghai, 200241, China;2. School of Risk and Actuarial Studies and CEPAR, UNSW Business School, The University of New South Wales, Sydney, NSW 2052, Australia;3. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia;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 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. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1;2. School of Accounting and Finance, University of Waterloo, Waterloo, ON, Canada N2L 3G1;1. Nova University of Lisbon — Information Management School (NOVAIMS), Portugal;2. University Paris-Dauphine, LEDa, IRD, UMR 225-DIAL, Paris, France;3. Smith School — Oxford University, United Kingdom |
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| Abstract: | This paper is concerned with the valuation of equity-linked annuities with mortality risk under a double regime-switching model, which provides a way to endogenously determine the regime-switching risk. The model parameters and the reference investment fund price level are modulated by a continuous-time, finite-time, observable Markov chain. In particular, the risk-free interest rate, the appreciation rate, the volatility and the martingale describing the jump component of the reference investment fund are related to the modulating Markov chain. Two approaches, namely, the regime-switching Esscher transform and the minimal martingale measure, are used to select pricing kernels for the fair valuation. Analytical pricing formulas for the embedded options underlying these products are derived using the inverse Fourier transform. The fast Fourier transform approach is then used to numerically evaluate the embedded options. Numerical examples are provided to illustrate our approach. |
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| Keywords: | Equity-indexed annuity Variable annuity Regime-switching Esscher transform Fast Fourier transform |
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