Efficient valuation of guaranteed minimum accumulation benefits in regime switching jump diffusion models with lapse risk (2024)

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Authors: Zhimin Zhang and Wei Zhong

Published: 24 July 2024 Publication History

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    Abstract

    We present a streamlined valuation method for the guaranteed minimum accumulation benefits incorporated within variable annuity contracts. At each contract renewal date, the insurer updates the policyholder's account value to the higher of the guaranteed value and the equity-linked investment value. In addition, we introduce lapse risks into the variable annuity contract, modeling the lapse decision under the assumption of stochastic intensity. Utilizing a combination of continuous-time Markov chain approximation and the Fourier cosine series expansion method, we derive closed-form valuation formulas under regime switching jump diffusion models. Numerical simulations showcase the precision and effectiveness of the proposed approach.

    Highlights

    This paper proposes an efficient computational method for pricing variable annuities.

    Our results significantly improve computational efficiency compared to Monte Carlo.

    We introduce lapse risk and regime-switching into the paper.

    Our method can be used to calculate option pricing.

    References

    [1]

    Jennifer Alonso-García, Oliver Wood, Jonathan Ziveyi, Pricing and hedging guaranteed minimum withdrawal benefits under a general Lévy framework using the COS method, Quant. Finance 18 (6) (2018) 1049–1075.

    [2]

    Søren Asmussen, Applied Probability and Queues, Springer Science & Business Media, 2008.

    [3]

    Laura Ballotta, Ernst Eberlein, Thorsten Schmidt, Raghid Zeineddine, Variable annuities in a Lévy-based hybrid model with surrender risk, Quant. Finance 20 (5) (2020) 867–886.

    [4]

    Ning Cai, Yingda Song, Steven Kou, A general framework for pricing Asian options under Markov processes, Oper. Res. 63 (3) (2015) 540–554.

    [5]

    John C. Cox, Jonathan E. Ingersoll Jr., Stephen A. Ross, A theory of the term structure of interest rates, Econometrica 53 (2) (1985) 385–408.

    [6]

    Zhenyu Cui, Stephen Taylor, Pricing discretely monitored barrier options under Markov processes through Markov chain approximation, J. Deriv. 28 (3) (2021) 8–33.

    [7]

    Zhenyu Cui, J. Lars Kirkby, Duy Nguyen, Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps, Insur. Math. Econ. 74 (2017) 46–62.

    [8]

    Zhenyu Cui, J. Lars Kirkby, Duy Nguyen, A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps, Eur. J. Oper. Res. 262 (1) (2017) 381–400.

    [9]

    Zhenyu Cui, Jinhyoung Kim, Guanghua Lian, Yanchu Liu, Risk measures for variable annuities: a Hermite series expansion approach, J. Manag. Sci. Eng. 4 (2) (2019) 119–141.

    [10]

    Zhenyu Cui, J. Lars Kirkby, Duy Nguyen, Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations, Eur. J. Oper. Res. 290 (3) (2021) 1046–1062.

    [11]

    Robert J. Elliott, Lakhdar Aggoun, John B. Moore, Hidden Markov Models: Estimation and Control, Springer Science & Business Media, 1994.

    [12]

    Fang Fang, Cornelis W. Oosterlee, A novel pricing method for European options based on Fourier-cosine series expansions, SIAM J. Sci. Comput. 31 (2) (2008) 826–848.

    [13]

    Fang Fang, Henrik Jönsson, Cornelis W. Oosterlee, Wim Schoutens, Fast valuation and calibration of credit default swaps under Lévy dynamics, J. Comput. Finance 14 (2) (2010) 57–86.

    [14]

    Runhuan Feng, An Introduction to Computational Risk Management of Equity-Linked Insurance, CRC Press, 2018.

    [15]

    Runhuan Feng, Bingji Yi, Quantitative modeling of risk management strategies: stochastic reserving and hedging of variable annuity guaranteed benefits, Insur. Math. Econ. 85 (2019) 60–73.

    [16]

    Hans U. Gerber, Elias S.W. Shiu, Hailiang Yang, Valuing equity-linked death benefits and other contingent options: a discounted density approach, Insur. Math. Econ. 51 (1) (2012) 73–92.

    [17]

    Mary Hardy, Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance, vol. 168, John Wiley & Sons, 2003.

    [18]

    Yiming Huang, Rogemar Mamon, Heng Xiong, Valuing guaranteed minimum accumulation benefits by a change of numéraire approach, Insur. Math. Econ. 103 (2022) 1–26.

    [19]

    Junike Gero, Konstantin Pankrashkin, Precise option pricing by the COS method-how to choose the truncation range, Appl. Math. Comput. 421 (2022).

    [20]

    Boda Kang, Yang Shen, Dan Zhu, Jonathan Ziveyi, Valuation of guaranteed minimum maturity benefits under generalised regime-switching models using the Fourier Cosine method, Insur. Math. Econ. 105 (2022) 96–127.

    [21]

    J. Lars Kirkby, Hybrid equity swap, cap, and floor pricing under stochastic interest by Markov chain approximation, Eur. J. Oper. Res. 305 (2) (2023) 961–978.

    [22]

    J. Lars Kirkby, Jean-Philippe Aguilar, Valuation and optimal surrender of variable annuities with guaranteed minimum benefits and periodic fees, Scand. Actuar. J. 2023 (6) (2023) 624–654.

    [23]

    J. Lars Kirkby, Duy Nguyen, Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models, Ann. Finance 16 (3) (2020) 307–351.

    [24]

    J. Lars Kirkby, Duy Nguyen, Equity-linked guaranteed minimum death benefits with dollar cost averaging, Insur. Math. Econ. 100 (2021) 408–428.

    [25]

    J. Lars Kirkby, Duy Nguyen, Zhenyu Cui, A unified approach to Bermudan and barrier options under stochastic volatility models with jumps, J. Econ. Dyn. Control 80 (2017) 75–100.

    [26]

    J. Lars Kirkby, Dang H. Nguyen, Duy Nguyen, Nhu N. Nguyen, Maximum likelihood estimation of diffusions by continuous time Markov chain, Comput. Stat. Data Anal. 168 (2022).

    [27]

    Mikhail Krayzler, Rudi Zagst, Bernhard Brunner, Closed-form solutions for guaranteed minimum accumulation and death benefits, Eur. Actuar. J. 6 (2016) 197–231.

    [28]

    Harold J. Kushner, Numerical methods for stochastic control problems in continuous time, SIAM J. Control Optim. 28 (5) (1990) 999–1048.

    [29]

    Lingfei Li, Gongqiu Zhang, Error analysis of finite difference and Markov chain approximations for option pricing, Math. Finance 28 (3) (2018) 877–919.

    [30]

    Chia Chun Lo, Konstantinos Skindilias, An improved Markov chain approximation methodology: derivatives pricing and model calibration, Int. J. Theor. Appl. Finance 17 (07) (2014) 407–446.

    [31]

    Jingtang Ma, Wensheng Yang, Zhenyu Cui, Convergence analysis for continuous-time Markov chain approximation of stochastic local volatility models: option pricing and Greeks, J. Comput. Appl. Math. 404 (2022).

    [32]

    Anne MacKay, Marie-Claude Vachon, Zhenyu Cui, Analysis of VIX-linked fee incentives in variable annuities via continuous-time Markov chain approximation, Quant. Finance 23 (7–8) (2023) 1055–1078.

    [33]

    Antje Mahayni, Judith C. Schneider, Variable annuities and the option to seek risk: why should you diversify?, J. Bank. Finance 36 (9) (2012) 2417–2428.

    [34]

    Aleksandar Mijatović, Martijn Pistorius, Continuously monitored barrier options under Markov processes, Math. Finance, Int. J. Math. Stat. Finan. Econ. 23 (1) (2013) 1–38.

    [35]

    Marjon Ruijter, Mark Versteegh, Cornelis W. Oosterlee, On the application of spectral filters in a Fourier option pricing technique, J. Comput. Finance 19 (1) (2015) 75–106.

    [36]

    Marjon J. Ruijter, Cornelis W. Oosterlee, Two-dimensional Fourier cosine series expansion method for pricing financial options, SIAM J. Sci. Comput. 34 (5) (2012) B642–B671.

    [37]

    Vincenzo Russo, Rosella Giacometti, Frank J. Fabozzi, Intensity-based framework for surrender modeling in life insurance, Insur. Math. Econ. 72 (2017) 189–196.

    [38]

    Chi Chung Siu, Sheung Chi Phillip Yam, Hailiang Yang, Valuing equity-linked death benefits in a regime-switching framework, ASTIN Bull., J. IAA 45 (2) (2015) 355–395.

    [39]

    Qingshuo Song, George Yin, Qing Zhang, Weak convergence methods for approximation of the evaluation of path-dependent functionals, SIAM J. Control Optim. 51 (5) (2013) 4189–4210.

    [40]

    Domingo Tavella, Curt Randall, Pricing Financial Instruments: The Finite Difference Method, John Wiley & Sons, 2000.

    [41]

    Eric R. Ulm, Analytic solution for return of premium and rollup guaranteed minimum death benefit options under some simple mortality laws, ASTIN Bull., J. IAA 38 (2) (2008) 543–563.

    [42]

    Oldrich Vasicek, An equilibrium characterization of the term structure, J. Financ. Econ. 5 (2) (1977) 177–188.

    [43]

    Xiang Zhang, Lingfei Li, Gongqiu Zhang, Pricing American drawdown options under Markov models, Eur. J. Oper. Res. 293 (3) (2021) 1188–1205.

    [44]

    Yixing Zhao, Rogemar Mamon, Huan Gao, A two-decrement model for the valuation and risk measurement of a guaranteed annuity option, Econom. Stat. 8 (2018) 231–249.

    [45]

    Wei Zhong, Zhenyu Cui, Zhimin Zhang, Efficient valuation of guaranteed minimum maturity benefits in regime switching jump diffusion models with surrender risk, J. Comput. Appl. Math. 422 (2023).

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    Published In

    Efficient valuation of guaranteed minimum accumulation benefits in regime switching jump diffusion models with lapse risk (1)

    Applied Mathematics and Computation Volume 478, Issue C

    Oct 2024

    220 pages

    ISSN:0096-3003

    Issue’s Table of Contents

    Copyright © 2024.

    Publisher

    Elsevier Science Inc.

    United States

    Publication History

    Published: 24 July 2024

    Author Tags

    1. Variable annuity
    2. GMAB
    3. Regime switching jump diffusion model
    4. Lapse risk
    5. CTMC
    6. COS method

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