Valuation of Annuity Guarantees under a Self-Exciting Switching Jump Model

Charles Guy Njike Leunga () and Donatien Hainaut ()
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Charles Guy Njike Leunga: Université catholique de Louvain, LIDAM/ISBA, Belgium
Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2021025, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This article investigates the valuation of annuity guarantees under a regime-switching model when the dynamics of the underlying stock price follows a self-exciting switching jump diffusion process. In this framework, the intensity of shock arrivals, the return and volatility of shocks are modulated by a continuous time hidden Markov chain with a finite number of states. The interest rate is stochastic and correlated to the stock market. In an incomplete market, we define an equivalent martingale measure to price a variable annuity contract with a minimum guarantee in case of death or life. Under this equivalent martingale measure, we propose closed-form approximation formulas using the inverse Fourier transform technique. A numerical implementation highlights the impact of self-exciting jumps and economic regimes on the valuation of guarantees.

Keywords: Variable annuity; Self-exciting; Hidden Markov chain; Fourier transform (search for similar items in EconPapers)
Date: 2021-01-01
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