Valuation of Annuity Guarantees Under a Self-Exciting Switching Jump Model
Pages 963 - 990
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.
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Published In
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.
Publisher
Kluwer Academic Publishers
United States
Publication History
Published: 01 June 2022
Accepted: 18 January 2022
Revision received: 10 January 2022
Received: 27 February 2021
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