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
Donatien Hainaut: Université catholique de Louvain

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 2, 963-990

Abstract: Abstract This article investigates the valuation of annuity guarantees under a regime-switching model when the dynamics of the underlying stock price follow a self-exciting switching jump-diffusion process. In this framework, we add a jump component to a regime-switching geometric Brownian for large shocks on the stock price. The intensity of shock arrivals is a Hawkes process modulated by a continuous time hidden Markov chain with a finite number of states. The interest rate used for discounting is stochastic and correlated to the stock market. In an incomplete market, we define an equivalent martingale measure to price a variable annuity contract that guarantees a minimum living or death benefit. 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: 2022
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DOI: 10.1007/s11009-022-09931-8

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