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

Author

Listed:
  • Njike Leunga, Charles G.

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

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.

Suggested Citation

  • Njike Leunga, Charles G. & Hainaut, Donatien, 2022. "Valuation of Annuity Guarantees under a Self-Exciting Switching Jump Model," LIDAM Reprints ISBA 2022003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2022003
    Note: In: Methodology and Computing in Applied Probability, 2022
    as

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